Metals such as gold and silver were (and are) melted down all the time. If you didn't want to be left behind when when fashions changed you would take your silver to the silversmith to rework it. If you ran short of money your silver plate could be sold as bullion.

The need for gold or silver to make bullion and then coins is a constant drain on jewellery. Even as late as world war 1 women were being used to give up their gold jewellery to fund the war effort (Gold gab ich für Eisen).

Finally you have invading forces who didn't care about the local art or jewellery and just saw it as source of gold and silver. the Spanish in south America are probably the best known example but there Viking were much the same. This is a Viking hack hoard. Its a fairly random collection of (generally damaged) silver objects.

Gem can't be melted down but they can be reset (re-used in new and more fashionable items). They could also be sold and records lost. For example three large rubies call the three brothers were first known to be owned by Charles the Bold. They then went to the Swiss (war) then to Antwerp(purchase) from where they went to Henry VIII(purchase). They then passed down the English royal family until the civil war at which point they were pawned in Antwerp and disappear from the records. Do they still exist? Maybe but how would you tell the difference between them and any other large natural ruby.