I have actually done a tremendous amount of research on the repercussions of the Fourth Crusade on the Mediterranean world post-1204. My short answer is that the Byzantine nobility of Constantinople and the Greek population of the city fled to Nicaea, a nearby fortified city and ecclesiastical center in Asia Minor. The best contemporary Greek source of these events is Niketas Choniates, whose Chronicle was written after the displacement of the Greeks and provides some of the best nitty-gritty details of the Sack itself.

Byzantine soldiers who remained in Constantinople would have been slaughtered or at least their property would have been confiscated. Otherwise the Byzantine troops rallied around their lords at Nicaea and continued to be a thorn in the Latin Empire's side until 1261, when the Genoese navy helped them reclaim Constantinople for the Greeks.

The Dumbarton Oaks essay "Rialto Businessmen and Constantinople, 1204-1261" by Louise Buenger Robbert looks at the economic unviability of the Latin Empire, and one of Robbert's main arguements was that the Venetians and Crusaders never bothered to recreate the Byzantine fiscal beauracracy that had picked up and left in 1204. The imperial court and nobility of Constantinople had depended on the tax flow from the owners of giant estates surrounding the capital as well as from lucrative trade ports along the coast if the Black Sea. If this fiscal bureaucracy didn't continue to transport taxes to Constantinople, they must have either chosen to fund local Byzantine lords, or the imperial claimants who ruled the various successor states.

At Nicaea, Byzantine troops probably had the resources to rearm themselves and live relatively comfortably, although the call to reclaim their holy city no doubt was more influential than gold could ever be. Choniates makes clear in his Chronicle that the Sack of Constantinople, the desecration of her churches, the appointing of a Venetian patriarch, and the greed of the Frankish knights were a signal of the approaching apocalypse.

So in other words Byzantine troops temporarily retreated to Nicaea but were never detrimentally defeated to the point that they were not able to begin fighting again.

Edit: Check my replies below for a source list! Thank you for reading! Edit: Some Greeks remained in Constantinople, however they were a silent minority if anything Edit: adding more clarifications and things