I got insurance on my father's house during a year long process of getting it cleaned up and fixed to sell. I called about 3 different companies, and went with the cheapest one. I lived out of state, but had no issues locating a company. The only issue we ran into was that they would not start the policy coverage until a back door was replaced (it was a very old door with a non functional lock so the house was unable to be secured until it was replaced). Once we informed the agent it was fixed, it was all good.
I discussed up front with the agent the circumstances and they actually ended up selling the policy as rental insurance (like I was a landlord) since there was nothing in the house (no furnishings/property) just the house and property itself. It was pretty cheap actually.
If the house is truly selling one day after the policy lapse, I'd probably just risk it going without for that one day... but if you are too worried about it, then do call around and explain the situation. I'm sure some company out there would be happy to take your money for that one extra day.
And any insurance company - even the current one - would be fine with you getting a NEW policy on the house to insure it until it sells. They just won't extend the old one since it's technically a contract between them and your deceased parent, so of course they'd want to rewrite the policy due to the change in circumstances.
Some insurance companies will try to quote really high prices since it is a bigger risk as it is vacant, but just call someone else. Even if the best you can fine seems expensive, if it sells in a month or two, they'll prorate the amount and send it back to you.
