Yes.  The children will be responsible for paying the mortgage each month until the loan is paid off or the house is sold.If you live in California, it is almost always less expensive to put your house (and other assets) into a living trust and pass it to your children via the trust instead of by will ... a $300,000 house (even if it had a $299,000 mortgage) would cost a minimum of $9,000 plus court costs to probate; a trust should cost less than $4,000 (probably $1500 to $3000 depending on your particular circumstances).A trust has other advantages, too, but it would be too lengthy to discuss them here.The information you obtain at this site is not, nor is it intended to be, legal advice. You should consult an attorney for individual advice regarding your own situation.