Right of First Refusal or ROFR is built into all contracts. It gives Disney 30 days after an offer is submitted from the buyer to the seller to match the offer and buy back the property themselves. Disney uses this for two main purposes.
When you as the buyer place an offer on a resale contract, the contract is submitted to Disney Vacation Development (DVD), they have the first option to buy back the property at the same price at which you have offered to buy it. Two things can happen
(A) Disney takes the contract, in which case the buyer gets paid the same amount that you would have paid. You get your deposit back, but lose out on the contract and have to start the buying process over again.
(B) Disney waives the ROFR, in which case you would now be the buyer of record. The contract will typically procede through the normal channels. Usually it takes 2-4 more weeks for the contract settlement to complete.
Strictly speaking, Disney has at minimum 30 days to decide on ROFR. Technically if you read the fine print, they can take even longer but this rarely happens. Often it is shorter than 30 days.
This is a hard number to predict. Typically Disney takes back about 10-15% of all contracts in a given time period. If the price you have offered is unusually low, then that does increase the chances of Disney taking the contract. Otherwise, there is no set pattern. Some say they like contracts that are fully loaded with points, others say they like contracts that are stripped (points from current UY are gone). The truth is there isn't really a pattern. The only definite is that it seems Disney will not buy back contracts for resorts that are currently "live". So, for Spring of 2020 - that means Aulani and Riviera.