Later medieval Christians were absolutely not above giving God a little help in the relics department. For example, Christians believed one of the principle signs of a person's sanctity was the incorruptibility of their corpse after death. 13C "second Franciscan founder" Clare of Assisi was guaranteed to be canonized after her death, her sanctity was already so apparent in her lifetime. Yet local apothecary Thomas di Bartolomeo was still hired to embalm her body with herbal preservatives--giving God's preservation a bit of a boost.

So it's little surprise that, yes, the Shroud of Turin was repaired (or "repaired") not once but twice during the 16th century!

First, a fire at Chambéry (where the Shroud was then housed) in 1532 burned multiple holes in the shroud. In the next couple of years, local Franciscan nuns duly patched over the holes, sewing undisguised triangle patches into place. (Note that this is not the claimed "medieval replacement" repair, a claim that rests on 13-15C fabric being added to a 1C cloth).

Second, sometime between 1559 and 1578, what contemporary sources called the "painting" of Jesus on the Shroud mysteriously acquired clothing. That's right. The naked Jesus barely visible today and much more explicitly visible in early 16C illustrations, by the 1578 engraving of Giovanni Testa is wearing a loincloth. Pop historian Charles Freeman, who probably knows more about relics and their uses in the Middle Ages and Reformations than anyone else (although his interpretive framework has some problems), points out the reason for this change.

In the Counter Reformation, the Shroud became a key political tool of the Catholic Church, periodically placed on display to wow the crowds. At the Council of Trent, concluded in 1563, one of the decrees has banned (almost as an afterthought) "sensual allurment" or lascivia from religious art. Hence the more famous painting over of the full frontal nudity in Michaelangelo's Last Judgment. And hence, Freeman argues, the added loincloth in order to pacify the host of the 1578 exposition's "celebrity guest" presider, the Archbishop of Milan who had supported the decree.

In the Middle Ages, relics were alive. They bled, transformed, disappeared to avoid destruction, resisted destruction, swam, insisted they be kept in one place or taken to another, and multiplied. Medieval and early modern people had little qualms about supplying some help where help was needed.

To add to u/sunagainstgold's very good answer, the reliquary of Sainte Foy is a good example of how over centuries, alterations and additions could be made to reliquaries. These alterations and additions often happened after the relic and reliquary were translated (meaning moved from one place to another) and/or when the church in which it was housed and displayed gained prominence (many times because of a new relic that increased pilgrimages to the site) so that the church could afford to make these changes.

The reliquary of Sainte Foy (pictured here) is such a great example because the reliquary really is a hodge-podge of materials gathered and added over nearly a millennia. Sainte Foy (Saint Faith) was a young Christian killed in Agen during Diocletian's persecutions, and was thus one of the martyr saints from the early fourth century. It is known that her relic (her skull) was held initially or a few centuries later in a monastery in Figeac, where a basic reliquary container was created for the relic. This at the very least consisted of a wooden statue frame, and the reappropriated fifth-century bust of a male roman emperor (strange, no!?).

Then, after the construction of a monastery in Conques in the ninth century, monks from Conques decided they would travel to Figeac and attempt to translate the relic, hoping to successfully establish the site (reliquaries were needed in order for a church to become consecrated) and bring pilgrims and renown to Conques. The reliquary of Sainte Foy was sought after in particular since by this time, she had already become a sort of “fan favorite,” so to speak — martyred at thirteen, she was known for jovial, childish pranks and miracles. As /u/sunagainstgold mentions, relics were considered living objects. Thus, with regard to translation, if a relic did not want to be moved, it would not allow itself to be translated. The theft of relics was technically allowed in this sense, then, since the reasoning was that if a relic made it successfully from one church to another one, it wanted to be moved.

After being translated, the church at Conques added some additional flair to the reliquary in the ninth century (likely a metallic base over the eighth-century wooden one at the very least) and other pieces can be dated as late as the thirteenth and fourteenth centuries. Sainte Foy’s liber miraculorum (book of miracles) gives its own fascinating explanation for how the reliquary acquired so many additions: it was said that in addition to her jovial spirit, she was also very demanding and quite vicious to anyone who doubted her miraculous power or insulted her reliquary. Thus, she would appear to pilgrims in dreams and demand jewelry and precious stones for her reliquary either in exchange for a miracle, or as punishment for insult or disbelief. Anyone who failed to meet such a request would find themselves suddenly ill or gravely injured (one individual, for example, was spontaneously engulfed in flames).

I hope this is a helpful (if extraordinary) example of how living objects changed materially over time.