Yes, the estate can and should pay the mortgage to preserve the asset.If the named beneficiary does not want the gift, they would disclaim the interest in writing pursuant to local law and it would then pass to the next named heir or as part of the residuary.

If it is it sounds like this is the time that you really nail down the numbers and decide if its really worth pursuing.

I can nail the lathe to the rafters whereas you cant guarantee the tin will be screwed to the rafters without them.

I have pretty solid contractors for most other things but I can't seen to nail down a deal  on cabinets. 

The pile of nails is where the joist should be!

Both @Jay Hinrichs and @Brian Eastman nailed this. 

@Joe Villeneuve has it nailed.

@David Floyd, You nailed the issue. 

Tax attributes of the gain (i.e. short-term, long-term gain) that are deferred are preserved through the deferral period until income is recognized. 

In these cases its all about capital preservation..