Ideally, this shouldn't happen. A soldier is responsible for their musket and depending on the officers, they would either be informed "fix your musket after battle" or they could be threatened with corporal punishment (pre-Revolutionary) or some sort of work detail as punishment (Revolution to Napoleonic).

If the soldier has a broken musket, they obviously can't fire. They could try to filter back to the rear of the formation (as position wasn't precisely assigned) and either try to fix it (from a tool kit they carry) or just accept that it was broken and hope they don't have to fight anymore. After the battle they would fix the musket on their own and approach their NCOs or Company/Battalion quartermaster in order to obtain extra parts as needed.

A little follow up-question, if nobody minds.

Where did the infantryman go to fix his gun after said battle? Did every regiment have its own gunsmith who'd look after the regiments guns? If not, who makde sure, that the guns can be used again? Someone on the army level? Did this practice differ between armies of say Britain and France?

Also a follow-up - I've just muzzle-loaded my musket for the first time in this battle, but it didn't fire - it's been a rainy day and the powder inside the barrel is most likely wet. What do I do now, stand idle while my fellow soldiers fire the volleys, waiting for someone to get hit so I can use his weapon instead?

How much attention would it draw from my officers/NCOs?