He doesn't *have* to, he'll just be an undocumented/illegal* alien. Worst that'll happen is they deport him if he gets pulled by a cop for any reason, which would probably happen if he's on a valid visa anyway.
And no-one ever checks your visa expiry when you leave a country - been there and done that twice myself, even post-9/11 they simply tore out the visa and didn't look at it.
* There are actually differences in the US at least between being out-of-status (undocumented) and being an illegal alien; being out of status can, usually, be fixed given the right paperwork / money, but being illegal is a deport + 10yr ban - but being banned from israel probably isn't high on Eli's 'give-a-shit-about'ness scale anyway.