My sister's visitor

I don't know if this is the right place to post this but I am really unsure about the situation.
I am currently visiting my sister in Germany and met a cat that she sees around her place all the time and tells me about. He/ she is just sooooo adorable. The cat waits inside/ outside her building door to be let out/ in my the residents when they come in or go out. My sister's apartment is on the garden level and the cat appears when she cooks. My sister finds him/ her cute but she is not an cat/ dog person. A couple of days after I arrived I met the cat and he/ she was friendly. I said hello and the cat was so vocal. I got a bump on my hand when I extended my closed fist to greet the cat and then the cat allowed me to pet hI'm/ her briefly. My sister always said that the cat us shy. Now we do not know if the cat belongs to anyone - no visible id. I really do not know German pet culture enough but it does not seem that the cat's starving but according to my sister the cat was rather chunky and lost some weight in the past year (my sister's been in this apt for 2.5 yrs and has always seen the cat). No one in the building has a cat door or leave out a bowl of food / water outside the door. My sister has seen the cat walking around in the neighborhood. So in this situation, is it advisable to leave a little dry food out for the cat? He/ she definitely appears whenever my sister is cooking. The thing is, my sister may not be the most responsible of people to be consistent with feeding the cat. She is kind of scared to touch the cat (or any animal for that matter) and so vetting is not an option. In this case, will it be wrong for me to give the kitty some food and then hope my sister will continue it when I leave? She will for a while, am sure- she has all the best intentions but they vacation a lot and I can see her forgetting once in a while. Also they will probably move out of here in the future. Would appreciate you weighing in on the situation.

Thanks everyone for the advice. I am not going to start feeding the cat and I do not think my sister will. I really hope that the cat belongs to someone. I asked my sister to write to her landlord and ask if it belongs to someone in the building. She's seen the cat for her 2.5 yrs here but says the cat's lost weight, though it is not skinny now by any means. Also last night (nearly midnight) when we returned from a roadtrip (we were out since I last posted) the cat came inside the building when my sister opened the door and then when we were still bringing in the baggage, the cat left. Which makes me think that he/ she may not belong to anyone in the building and spends the night outside. It saddens me so much - especially since he/she reminds me of Hobbes. I leave for London in 2 days and so it will be upto my sister to try to find out about the cat, if she wants. I just pray that the cat is well and taken care of.

here he/ she is:Attachment 15517

The reason the pregnant issue did not come up was because my sister saw the cat chubby for over 1.5 yrs and it is only this past year that she's been saying the cat's lost weight.
The more I hear and see, I someone feel that the cat's without a home. He/ she is outside all times of the day and night. My sister will write to the landlord and ask some neighbors.