As Brian says what happened on each battle's aftermath would depend on a number of factors - whether the sides managed to disengage cleanly and perhaps withdraw in order, or if panic* set in, one side might have the energy to hunt down and slaughter the other (Rivers and other natural obstacles made ready made killing grounds - so for example the Bannock of Bannockburn and I think the bloody meadow in the aftermath of the Battle of Towton
https://en.wikipedia.org/wiki/Battle_of_Towton#Aftermath was another notable slaughter ground.)
Other armies fought to extinction knowing, even if they knew their cause was lost, because that they could not extricate themselves or they had the spirit to resist capture (the destruction of the royalist infantry at Naseby springs to mind, but there are innumerable examples of this - Flodden for example.)
If the fleeing army soldiers weren't rich enough to capture, then generally I'd expect that they would slaughtered if the chasing army could get them - again from memory there are plenty of lovely quaint churches and buildings with very bloody histories as fleeing men exhausted men tried to find sanctuary, only to find the the 'no quarter' rule was still being applied by their enemies. From a purely strategic point of view I'd guess that would make sense, because if you let all these enemy escape, then they could regroup and fight another day.
As you will probably know from the Civil period being captured could be a horrendous experience and many captured soldiers would die of disease and ill treatment as they were thrown en masse into cells. This of course continues to the modern period - there is the harrowing footage of the some of the hastily constructed German PoW camps that they set up for the Soviets in WW2 - basically a huge hole in the ground, fenced off and thousands of Russian soldiers exposed to the elements and being essentially starved.
I can't think of a specific study of battle aftermaths, so I'd suggest getting accounts and books on specific battles - normally these will go into some depth on the aftermath of that particular event.
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* From time immemorial, when fighting relied on the spear and sword, rather than the firearm, it is generally the
back of the army that causes routs - the ones that are
not engaged with the enemy and have little to do but worry and fret about what might happen. So for example in the back of phalanxes/pike squares - the ones at the front are too busy fighting for their lives to worry about panicking...well only when they glance around and discover that all they can see are their colleagues dropping armour and weapons and fleeing away from them!