I think you've missed the point a bit, as we're kicking Corbyn not the homeless. It's the message that he's sending, that you don't have to bother because the government will look after you. That's what's wrong!
I have an (ex, fortunately) relative who genuinely believes that the state should pay for her, and she should not have to work.
To assist her with her dream, she ensured she got up the duff and had a mixed-race child, as apparently that helps. That was 15+ years ago, and still she hasn't worked, and receives enough benefits to pay for her 3 bed, state provided home. When the government a few years ago started making noises about getting people back to work, I've never seen her so angry, completely oblivious to the fact that it was unfair that people had to work so she didn't have to get off her lazy ass.
She always votes Labour, moreso since the death of New Labour.
As you say, that's wrong. But its the message being sent out by Corbyn
As for sympathy for the homeless, I've been in a position where I nearly did have to sleep rough, but with only an hour or so to spare, managed to sort out cheap digs for a few weeks until I was able to sort (afford) something more viable. Yes, it was significantly out of town, so I had to get up stupidly early to get to work, and get home stupidly late, and cook baked beans by dangling the can in a kettle, and eat out of the can, but I was prepared to do that.
So, as DG says, its in the Dictionary...