I feel this gets rarely mentioned, but a big battle happens, lots of people die, the winning army marches on, but what happens to the remains of the battlefield? Were the losing soldiers scavenged, buried and/or burned? Was it done by members of the army or "locals". Are there records of big losses having a noticeable impact on the metal economy of a region (based on my knowledge, getting iron/steel required a lot of work). If the answer is too complicated long, I'd be happy to get pointers to more detailed sources.
I would focus on the archaeological process in which a battlefield site is conformed and how it is affected by the successive plundering and scavenging done by soldiers and communities. Although I’m not an expert on medieval history some of the examples will be focused in ancient history yet I consider them quite universal in terms of behavior and actions by the soldiers and armies.
When we examine a battlefield we have to understand that it is slowly affected by human actions over a long period of time. The first pages of the study of military equipment found at the site of Baecula by Professor Quesada is an excellent overview of this process. Considering that is written in Spanish, I will sum up some of the main points.
The first plundering of the site is done by the army that stays in the area. This can be a thoughtful action or done with haste. Here aspects like strategy, military objectives or the actions of the other army will determine the time spend in the site and, therefore, the intensity of the scavenging. It will focus on the areas where the soldiers think they can find more elements. This means that the areas with the higher mortality or were the fight has been harder will be the ones most looked by the soldiers, as the presence of soldiers it will be higher. Paradoxically, this will affect how and where the remains objects can be found. As the areas with a higher concentration of objects is the one first checked, normally the marginal areas are the ones that can potentially yield more results over time.
Obviously, the plundering done by the soldiers will focus in elements that they could reuse, like armor and general equipment and anything that can be sold. After Waterloo, the price of several objects went down as the soldiers started to sell all the plunder. Also, you can expect that some fragments or elements of the equipment can be looted by sentimental reasons. The way this is done is difficult to assess but, for example, after Teutoburg, the Germans collected and spend some time processing what elements they were interested of the legionary equipment.
The treatment of the death will also be determined by the time expend and, logically, by their status. In case of a hurry the death can be abandoned like the Macedonians that died on the battle of Cynoscephalae, who 20 years later remained unburied. If not, some high ranking figures could be buried or at least their corpses picked by the winners. The treatment of the enemy could also be determined by the needs of the army. One of the best examples if the mass grave at the battle of Visby (1361) in which nearly 1.100 individual were buried along with their clothes and parts of their equipment. In some cases, if the death had thigh connections with the surroundings it could be expected that some people will come later and bury them. This is the case part of the population of Maiden Castel after it was taken by Vespasian which show some sort of ceremony, even though their burial is somewhat hurried and anormal. In the mass grave at Lützen (1632), the disposition show that the dead soldiers were thrown from different points, which seems to confirm a burial done as fast as possible. Also, they have been plundered of anything of value before they were thrown.
Once the armies have left the area, the local populations can do some scavenging. This is a long process as the objects and elements that could hold some valor can be difficult to find. Nonetheless this could yield some findings, specially coins and small objects, harder to find by soldiers. If the area remains cultivated objects could resurface periodically yet, over time, they will be significant smaller and least defined. Expect, after some decades, to find mostly small and very fragmentary objects.
Concerning the possible impact on the economy of an area I cannot define it precisely. As I have stated, medieval period is not my area of expertise but I hope that all the description of the looting post-fight can be enlighting.
The references employed in the post:
Forsom, Eva & Boel, Lene & Jaque, Bo & Mollerup, Lene. (2017). The death of a medieval Danish warrior. A case of bone trauma interpretation. Scandinavian Journal of Forensic Science. 23. 10.1515/sjfs-2017-0001.
Nicklisch, Nicole, Frank Ramsthaler, Harald Meller, Susanne Friederich, y Kurt W. Alt. 2017. «The face of war: Trauma analysis of a mass grave from the Battle of Lützen (1632)» 12 (5):1-30. https://doi.org/ttps://doi.org/10.1371/journal.pone.0178252.
Quesada Sanz, Fernando, Francisco Gómez, Manuel Molinos Molinos, y Juan Pedro Bellón. 2015. «El armamento hallado en el campo de batalla de Las Albahacas-Baecula». En La Segunda Guerra Púnica en la península ibérica. Baecula, arqueología de una batalla, editado por Juan Pedro Bellón, Arturo Ruiz, Manuel Molinos Molinos, Carmen Rueda, y Francisco Gómez, 311-96. Jaén: Universidad de Jaén.
ROST, A. & S. WILBERS-ROST, 2015. Looting and scrapping at the ancient battlefield of Kalkriese (9 A.D.), in La Segunda Guerra Púnica En La Península Ibérica. Baecula, Arqueología de Una Batalla, eds. J.P. BELLÓN, A. RUIZ, M. MOLINOS, C. RUEDA & F. GÓMEZ CABEZA. Jaén: Universidad de Jaén, 639–50.