IF that went down, and unlike some of the others here, there is valid speculation that it could happen. Barber is going to get a good paycheck this time around an IF Dallas were to move up and get DM, that salary is going to be huge. The Cowboys are not in pristine cap situation right now. Although a trade involving Barber is slim is does have some sound background to it. IF they moved up and let's say Schefter is right that it is Barber and 3 picks. Barber would have to be tendered first which the Cowboys currently have 2 days to do so. After the 28th mid-night, the Boyz can no longer tender him a restricted free agent contract which means they no longer get full compensation. In that event, Barber could sign with anyone and the Cowboys would receive a pick corresponding to the draft round Barber was taken in.
Assuming that the Cowboys will in fact tender Barber as so far no contract has been signed by Barber for an extension, the Cowboys could use that tender to trade with Miami. Barber would simply need to sign the tendered agreement and then work out a new contract with Miami. That is the easiest as the only guarantee is the tendered amount. However, the downside is that should Barber be tendered at any level and receive an offer from another team, then Dallas would have 7 days to match that offer which could cause a problem if the contract is non condusive to something the Dolphins would want to pay.
IF Barber is traded in a package to move up, look for it to coincide with Barber doing one of two things, signing a tendered contract that has no signing bonus or two, signing a contract worked out with the Dolphins. Where Barber is given permission to work out a contract with the Phins then is traded to Miami and his rights are thereby revoked. The latter is less likely early, but is more likely closer to the draft.