Unless the lender can be persuaded that the borrower can finance the
on-going mortgage liability (e.g. interest and any capital repayments),
which is likely to include guarantees from the individual trustees,
personally, it is unlikely that borrowing can be obtained.
Do the other children need financial support, or would they be willing
for the child in question to receive the primary benefit during their
lifetime? If so, then the whole estate could be subject to a
discretionary trust (over income only) with all 4 children being
entitled to capital on the winding up of the trust.
The full value of the trust could then be applied for the purchase of
property, with the agreement of the children, and any income could be
shared between those children not occupying the house.