I am not sure if 170,000 will buy a starter home these days.
Any cash arriving into her bank account will not go down well with SW.
You are probably better off to gift her the home.
I am sure others with more experience with SW will be able add their comments.
JSA is means-tested. JSB is not means-tested.
It sounds like she is on JSA.
If she has 170k, her JSA payment would be cut.
If she receives a gift of a house, and then lives in the house, I think her JSA payment would not be affected, as a PPR is not included in the means-test.