good for you to want to rehome and older cat, i have done it in the past and havn't regretted a moment.
In my case Gennie was 15 when I took her on and the re-homing centre told me she would last
just 6 months due to her age and kidneys. sadly she passed away last year at the grand old age of 19
but that was 4 years more than they gave her, so I am content that her last years were in comfort and
appreciated by her.
I digress
what you should do when you go and see the cat is
not approach it, sit down and let it come to you.
you can encourage this by making eye contact and then looking away.
to a cat this is an invite to approach, you may have to do this several times.
ask the owners about past medical care, has she any ongoing illnesses like kidney problems, arthritis, heart mummers etc.
has she ever been involved in a road accident or run away. (not that any medical problems should put you off, but you need to know to provide adequate care and your budget may not cover long term vet bills)
what kind of personality is she, aggressive, dominant, shy, loving etc.
basically get to know the cat as much as you can and if you have any doubts tell them there and then,
if they can't help make you certain this cat is for you, please decline to take it on. this will give them plenty of
time to find someone else.
HTH