Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
I don't know the answer to your question (but if the delay/cancellation is due to weather, I would not expect free lodging for the night).
However, depending on exactly where you are starting from, and what time you can leave, it night make sense to:
1) Take Amtrak from EWR, NWK, or NYP to Boston; or
2) Take NJ Transit and the LIRR from New Jersey to Woodside, Queens, where you can either take a taxi to LGA, or the Q70 Limited bus to LGA for the Shuttle.