homeless lady

Not sure if I have the right forum. I need some advice.

A 60 year old lady has been sleeping in the external car park of
my appartment blocks for at least 4 weeks now.
She sleeps there at least 5 days a week, she gets there around 10 pm and leaves in the morning anywhere between 7-9 am. The car park is sheltered from the weather and from prying eyes. I go down stairs and converse with her for 5-10 min when ever I can.
I have attempted to find out why she has nowhere to sleep and how she ended in this situation, but have had no success.
I have resorted to just excepting her and her situation and have become very fond of the old cat.
She is very witty and always manages to get a smile out of me.
From what I understand she is well known in the area and everyone loves
her.
She loves a drink and a smoke, I have taken her food several times
But she won't eat it,
After numerous attempts I worked out she eats sausage rolls so I bought a packet from coles and just microwave one for her every time I see her down stairs.
I have given her 2 very warm jackets that I didnt really wear that often and my wife had some singlets and pants she could spare.

My dilemma is that she sleeps on the concrete and refuses to sleep anywhere else, I have given her 2 thick blankets to lay down but she keeps on losing them. The problem is they are to big and when she attempts to tie them to the back of her bike they end up flying off.
I suggested to the wife that maybe I should buy a single blow up matters,preferably foot pump, but the wife thinks shell just lose it.

Any one have any ideas on what would be the best solution?

I should add a few of the residents in the block are not to pleased on seeing her there in the morning on there way to work. She had a large cardboard to sleep on but someone quickly got rid of it, I'm assuming in an attempt to get her to go somewhere else. Every time I see her Sherman repeats the same thing " someone took my cardboard".

I reallydo want to try and make her sleeps more comfortable, if anyone has any ideas it would be a great help.