Exactly, Geroff. We rented a house where the neighbour kept trying to do this to the LL, who continually refused his requests because he'd have trouble getting back his stuff. He instructed us not to allow him to borrow any of the tools or things he, the LL owned - he had canoes, sea kayaks, bikes and other such items in his garage.
So LL moved abroad a couple of years whilst we let the house. I guess the neighbour thought this was a carte blanche to try to help himself to LL's things. But we kept everything locked.
LL's lawnmower had broken and he purchased a new, £400 one he wanted online as we were looking after the quite large garden. DH used it a few times and neighbour poked head over fence, 'Oh, a new lawnmower.' DH, 'Yes, it's LL's lawnmower.'
One evening he went to mow and the mower was gone out of the shed! And there was another lock on it! WTF? We called the cops and reported it.
Neighbour had come when we were out, cut the lock off and replaced it with one of his own!
And he had to nerve to be affronted when we told him the thing had been lodged as stolen and we would now have to tell the cops the whole story.
Needless to say, once they paid him a little visit, he backed off with his borrowing requests.
LL was livid!
People try it on. 'NO'.