My grandma passed last month & I was forced to take her cat.  It's 14. Cat is friendly, female, not large. In April we had to put down the cat's brother. Both cats & my grandma were a family for 14 years.
So I get the cat to my house. After a few days it comes out from under my bed, pokes around, eats, seems to be adjusting.  
However the cat will not leave me alone.  The cat follows me through the house. Will jump on my bed, purr, rub against me waking me up, meow. I half asleep pet her, fall back asleep & then it happens over & over all night. If I'm in my office, she jumps on my desk & walks across my keyboard & does the same thing.  If I'm watching TV will again jump on the couch & do it there too.
The cat did not behave this way when visiting my grandma.
Is this some sort of emotional distress the cat is going through?  Suggestions? Is this just how some cats get?

I'm not a cat person. As I said I was forced to take her.

Yes, I had a cat like that.  Cats can go crazy after the death of a human.  It took one of my cats 6 weeks to get over the death of my mother.  I don’t think she ever really recovered as she died within a year.  At least she got back to fairly normal for several months.

She is bonding. Give her a chance.  Eventually she will become more aloof.

A change in behavior -including increased need for attention- can be an indication of illness/distress.

With the recent change in circumstances it doesn't seem strange for the cat to be really attached to it's new, and only, friend.

I would be tempted to just see where things settle over the next week or two.  Never a bad idea to get a check-up - and would definitely go that direction if there is any other indication of difficulties (change in litter box habits/output, eating, grooming, etc.)

Not a veterinarian, just a very long time cat owner.

Of course she's distressed! Her human mama isn't there anymore, she's been moved to a new home and surrounded with new people and her heart is broken. You have shown her a lot of affection, and this is what she needs right now.

She'll "settle down" in a few days or weeks as she gets used to her new surroundings.

Exactly what others have said.  While cats may not understand death like humans, they understand it some level.  Your new to you cat is grieving in its own way.  You are a familiar person who the cat recognizes as part of the "family" so it's bonding with you because it's sad and you are the one that brings it comfort.  

Just show it affection when it comes to you.  If you're sleeping, you can give the cat a quick scritch and then ignore it and it'll settle down.  If you give it too much attention while trying to sleep it will continue that behavior.  The rest of the time, give your kitty some affection when it wants some and soon it will become comfortable enough to do normal cat stuff.  

You should feel honored, that poor cat is also having the worst days of its life and has chosen you to comfort it.  That comfort and love goes both ways so enjoy your new friend.

My MiL's cat was like a ghost at her cigarette smoked filled house.  Never saw it.  

After she (MiL) passed, the cat lived with us.  Became a sweet, loving cat.

Environment.

What you are describing is normal cat behavior with their primary bonded person. The cat likes you. Often if you reciprocate the greeting behavior the "in your face" part of it stops. When they come up and get close, give a pet and offer a place to hang out nearby. Ignoring them often makes their affection more demanding.

Your choices are:

a) decide you like the cat back and train each other not to be annoying
b) get someone else in the household to bond more with the cat (in which case the cat will leave you alone mostly)
c) rehome the cat

There are lots of old ladies that lose their cats before they die, ask around your church/social circle where old people are and see if one wants it. The cat I rehomed from a friend with my mom has made her life much more wonderful again. It was worth the effort to see the old lady happy about hanging around at home a lot. It's an older cat so is less of a commitment and PITA than a kitten for an old person.

Cat has to stay with me.  

Guess I'll need to take this option.  I never had a pet of any kind, new to me.

Take her to the vet for a wellness check. Enjoy your new friend!

Good of you to take care of her. Enjoy your new friend. She’ll probably settle down.

Do you play with her? Most cats like to play. It’s part of their hunting instinct. In my experience, cats usually do well with being confined to a single room during the night, especially when adjusting to a new home.

I’m not an expert, but do have 50+ cat-years of experience. Your efforts will be rewarded many times over.

$300 vet bill later, cat is fine no problems.  I changed her food though. Vet recommended. The dry food & wet food. Using fancy feast for both, she likes it & so far has curbed the puking. I think it was the dry food she was eating.
Still hasn't calmed down much.  Now the cat is pooping right outside the little box.  I don't know why, box is clean, maybe it's a smell?
I'm not home till late maybe because she's alone?  I try to play with her, but she's uninterested most times.  She'll swat a few things & then walk away.

Was she an outdoors cat or did she come into contact with them or share a litter box with them? Often, but not always, going just outside the litter box indicates discomfort while pooping. This could be due to parasites (worms, giardia), or maybe the Fancy Feast doesn’t agree with her. What worked best with my girl who lived until age 18.5 was Tractor Supply’s “4Health” brand grain-free wet food. Most of her teeth were missing so she had a hard time eating dry food. She loved the taste and her poop was firm and not overpoweringly smelly. But you may want to bring a fresh sample to the vet for testing.

Pooping next to the litter box is the cat telling you she's upset about something.  Cats crave consistency so develop some daily rituals to help her settle into a routine.

Grew up with cats, always had them in the home. My best guess is the cat realizes the new situation and is trying to gain your frined ship. It sees you as the decision maker and wants to be considered by you the best way posible. This sounds like a situation with my cat. When I take my cat with me to my second Property the cat is super affectionate. ALways wanting to be on my lab or engaging with me. not like that at all but for a few minute a day when at my work location.

She lost and alone losing her human


She wants love


The pooping outside the box is stress


Give her attention and when you watching TV call her over and pet her


Always 3 steps when a cat is in a new place


3 day to decompress

3 week they watch and learn

3 month they then realize there home

Updating...
Behavior is the same. The cat is now under my feet all the time, and if I ignore her, she starts to meow & will run in front of me swatting my feet walking through the house.  If I'm not in the room the cat searches for me & then gets in my way for attention. Like as I write this from my office desk, she has jumped up on my desk & is purring & rubbing all over the place.  I kick her off & she comes back a few minutes later.
The cat still is uninterested in toys,(not even a laser pointer), I tried to give her catnip, she sniffed it once & will not go near it again. But will stretch out over the scratcher's wanting to be rubbed.
She now destroyed the arm of my couch. I had to put plastic covers on all the furniture corners to prevent anymore damage. Puking has improved.  Once in a while she will.  That is an age thing from what the vet said.
The cat just seems to be lonely, since no one but me & my GF are there. At diffent times.  My cams have observed the cat just sleeps all day till someone gets home.
As in life I'll have to just deal with it.

She needs a friend.  Go to the shelter and look for a sociable senior male.  Having someone to interact and curl up with while you are out should reduce the neediness and anxiety.

I tried to give her catnip,
Try Silvervine. It's available at chewy.com. I've got 6 cats; the ones who don't respond to catnip love the silvervine.

eta
Chewy.com is a terrific source for pet-related stuff, food as well as info. We have their food delivered; it doesn't cost any more.

Fancy Feast is "some real quality shit" (quoting a movie). Good move on the switch. With the kitty's age, she's basically on extended hospice. Give her a good life, clean her litterbox daily, and you guys will be alright. No need to get a companion at that age, well, maybe, if you were more experienced with animals.. just buy a feather-on-a-string toy (don't let her play it with it without your supervision though!) or a cheap laser pointer. Have fun!