How did Jack Crawford know Clarice was in danger once the FBI realized the house in Illinois was empty?

While this appears to be a story hole, the fact is, Clarice has out-smarted Jack Crawford a couple of times, and has proven to be insightful. When Hannibal tells her to 'look inside yourself', she correctly deduces that 'Yourself' is the name of a storage house, and she goes there and looks inside. She also has the insight when Jack speaks to the other officers at the morgue, when they are examining the body of the girl, that he spoke to her in a demeaning way, and it set a bad example for the other men. Then she had the insight into the fact the killer is using the girls to make a suit of their skins, she may have acted on this. He can assume she is ahead of him once again, and has correctly interpreted information she had, and acted on it. While he has no direct evidence she is somewhere else, it is a logical assumption, given her past history, and given the fact he incorrectly interpreted the info he had.

It's an error. A cut scene had Starling tell Crawford she thinks the killer is in Belvedere.

The longest scene extension takes place before Starling goes to Belvedere. There is a new scene with Starling, Crawford, Burke and Krendler in the Workprint. Starling mentions, that the killer might be from Belvedere, which was implied by Lecter. Krendler appears skeptical and argues with Crawford about Lecters escape. Burke suspends Starling.

Then Crawford and Starling are leaving the building. Starling appears despite her suspension determined to go to Belvedere. Crawford gives her some money and his number.

After her excited call and finding the Calumet City house empty, Crawford fears she might really be close to the killer. His fear makes sense knowing Lecter pointed her at the killer and doesn't otherwise.

I think the audience doesn't usually recognize the unsupported deduction because they're distracted by the scene's big fake-out and they know Starling's in the right place.