We had a similar issue happen when we purchased a house. The seller wanted to move the closing date back, but they asked us if we were okay with that beforehand and we had to sign an extension.
The closing is a legal engagement, complete with lawyer and contracts with the date already filled in. You have probably already paid at least some money into it. Even if it's not written down, if you have a verbally agreed upon date for closing, then the seller is obligated to close.
HOWEVER, the majority of closing contracts have an "on or about [the date]" clause, which means that the buyer/seller has 30 days to close if they miss the original date. Have you talked to your lawyer/agent and asked them to contact the seller?
The buyer and seller do not have to be in the same room for the closing, so why don't you explain your issue to the seller and offer to go through with your side of the closing on the scheduled date. The seller can provide you with the keys to the new place and sign the papers with he/she returns from their trip.
You are in a common situation (a really crappy one). Although it doesn't help you now, the next time you buy a home, be sure to give yourself some "out" time on your lease. I wish you luck!