Title commitment gap issue (Texas)

[Hend Harb]

We're a couple of days from closing. According to the title company the title commitment effective date can't be updated. They stick with the last date the country clerk database was updated. In our case, the last date it was updated was the 17th.

So what happens if something comes up between 17th and closing day? 

Shouldn't there be some sort of a gap insurance?

For reference, we're in Texas. 

Thanks