I can't answer this question from the perspective of the average medieval peasant, but I can give some information about the medieval Roman (or Byzantine) state and how they dealt with wounded during campaign.

To start I want to give a bit of background on the combatants I'm talking about. In the 10th century CE the standard soldiers of the Byzantine Empire were the Stratiotai. Stratiotai are distinguished from free peasants by their military service, service that came with certain economic, social, and legal benefits unique to the them. That being said, most Stratiotai were still farmers, farming plots of land next to their peasant neighbors. Hopefully this qualifies as close enough to your question to be helpful, but I want to make sure the distinction is apparent.

On campaign, Stratiotai were required to equip and provisions themselves. While the state, family, or community would assist in documented situations, the expectation was the solider would show up when summoned for campaign prepared. For example, the Praecepta Militaria lays out the following recommendation for equipment alone:

• short tunics extending to the knees, of cotton or coarse silk.

• short boots folded up to the knees or unfolded up to the thighs.

• thick caps of felt fastened over their heads with bands of cloth.

• sword, axe, or iron mace. Stored at the waste on a belt.

• sling stored in the belt.

• Shields no smaller than six spithamai.

• thick and solid spears, from twenty-five to thirty spithamai in length.

In addition, soldiers were required to bring provisions and the means to carry them. Once again from the Praecepta Militaria,

"If possible, they should travel everywhere on foot, each pair of men with one mule to carry their shields, spears, and provisions. "…"each group of 4 must have one man whose responsibility it is in time of battle to watch over their animals, baggage, and provisions. Those on foot unable to keep up with the cavalry because of the length of the march or fatigue should have an extra mule each to carry him and bring along their provisions. Their attendants must follow on foot. "

Not only were more obvious things like equipment and provisions required, but also pack animals and potentially servants could be shared between groups of soldiers. Speaking of groups it's important to understand how these soldiers were organized. The most basic organizational unit of the Byzantine army during this period was the banda. This unit changed in size over time but the Praecepta Militaria mentioned about 50 men. It also mentions "see to it that kinsmen with kinsmen and friends with friends are assigned to each one so that they live and take meals together in camp, on the march, and everywhere. " By now we're starting to paint a slightly different picture than the lone peasant whisked away to war in a far away place alone and with nothing but the shirt on his back. In the Byzantine army of this period we have groups on kinsmen, or at least men who were familiar with each other, receiving the muster and marching to war together as a cohesive unit. Well equipped and provisioned, likely with horses, pack animals and potentially servants to help on the march.

If one of them was to become wounded in battle, we can look at an earlier source, the Strategikon, for insight,

"In addition to the above, either or ten of the less skilled soldiers in each tagma should be assigned as medical corpsmen to each bandon, especially in the first battle line. They should be alert, quick, lightly clothed, and without weapons. Their duty is to follow about a hundred feet to the rear of their own tagma, to pick up and give aid to anyone seriously wounded in the battle, or who has fallen off his horse, or is otherwise out of action. "

And a later source, an anonymous treatise known as Campaign Organization and Tactics, for what happens after battle,

"on the march into the enemy's country the monoprosopa (wagons and extra horses) carry the armament and all the other siege equipment. But when they leave it, most of the missiles, and the other equipment, and arms will have been expended. The monoprosopa should then be divided into three sections"…"the third should go to the troops in the saka, so that they can convey the wounded, those who are so weak they might fall behind."

Unfortunately, I don't know of any Byzantine sources that directly mention how wounded soldiers are returned home. That being said, we have enough evidence to piece together at least some idea. Byzantine soldiers went to war with their kinsmen, generally from the same town or geographical area as them. They also brought servants and pack animals. It seems likely that if the corpsmen were able to retrieve a wounded soldier from the battlefield and get him back to camp, they had spare pack animals, wagons, and assistants to see to it that that man received basic care and transportation until the campaign was over. At the conclusion of a campaign, it sounds plausible that the banda returned home together, using these same resources to assist any who were too injured to make the journey on their own.