No, until they own it, they can't deduct expenses.
"Stepped-Up Basis" is not a bad thing. The higher the basis when you get something, the less capital gain you need to report when you sell it.
An inheritance does not trigger federal tax, only when you sell the item you inherited might there be tax.
Example:
If your parents bought a house for 100,000 and it's worth 200,000 when they pass, the "Stepped-up basis" would be 200,000.
If you sell it a year later for 225,000, you have 25,000 capital gains, rather than 125,000 capital gains if you had paid for it originally.
We deal with Federal Law here. Real Estate is governed by the State. You really need to speak with a local real estate attorney to make sure the title was held in a way that the house was inherited (it sounds like it was) before making any assumptions.
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