If your question relates to ETOPS critical fuel scenarios then my understanding is that these are only relevant to pre-flight planning. Once you are airborne, the CP and ERA fuel calculations cease to have any effect; in other words, if you calculate in flight that your fuel at the CP will be less than the ETOPS requirement you can still proceed, as the chances of an actual engine failure or depressurisation at the CP is deemed to be vanishingly small.
I suppose it's a bit like the difference between the MEL and the QRH. Dispatch under the MEL is more restrictive than continuing with the same failure after you are airborne.
I am new to ETOPS but this is what was covered during my training.
Of course, the PIC always has the final say and if he/she feels that the fuel shortfall is too much in relation to the planned flight routing still ahead of the aircraft, he/she has the right and responsibility to come up with an alternative plan of action. Just because it's legal, doesn't always make it safe.