Furloughed employee about to start a new job, can I simply tell my current employer I found alternate work the Thursday/Friday before the start date?

The furlough period is expected to end on 5/31. New job starts on 5/18. Main reason I want to notify later is to continue getting unemployment benefits. However, I don’t really want to burn bridges. Some people said screw my company I don’t owe any obligations, but again I do want to use them for a reference. Thoughts?

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