The pay later option guarantees the fare, so even if seats are gone in the same fare bucket, the price is not expected to change much (only fluctuate due to taxes). However, in rare cases, the price of the fare itself may change, which may explain a $2K price change.

For example, suppose you book a J ticket under a fare called JCHEAP for $2000, and it's kept on hold. If tomorrow J seats will no longer be available, the next bucket may be K, and the price can be, say, $4000, but with the pay later option you still have your J booking in place, so no price change. But the airline may decide to change the price of JCHEAP from 2000 to 3000 (or even drop the fare altogether) with no advance notice, in which case your J ticket may be priced higher.

The short answer is that the pay later option very likely, but not 100%, guarantees the price.

Shuly