The hospital won't have a lot on hand, they do for once or twice but eventually diversion gets noticed if it happens over and over. Depending on what they need, they might have to get it prescribed and have it filled at a pharmacy - some pharmacists and some doctors will get samples which can cover people (my ex used to get their psych meds from a psych with a shitload of samples). In this case, they might be taking Zofran before a chemo cycle to help with the nausea and might be getting it through a pharmacy rather than at a hospital.

Nurses sometimes slip em meds but that counts as practicing medicine without a license if they don't have an order or a prescription (Ive given plenty of left over ventolin puffers or liquid oral vitamin d during discharge, cant give it to anyone else and they have a perscription for it otherwise its going in the trash). Doctors don't generally give any medications, just the orders for them.