Say you're short the put vertical. The thing goes deep ITM and you're assigned on your short put. You're still long the deeper put. The assignment results in a synthetic long call that's ostensibly worthless (long shares + long put). There is no risk to the assignment other than microstructure.
Assuming it crossed the strike price of the deeper put, it could be a few points OTM and right at expiration day or within a few days. so you are at risk at having a shit ton of stock put to your account and not enough equity to cover assignment.