Can you be fired or get in trouble if a till is over?

Hiya I'm making this question on behalf of my cousin who chewed my ear off for the last half hour on the phone because he's anxious over his day at work... He's got no one else to talk too so I thought I'd ask on here.

He had this customer and he was out of £5 notes so he called his boss; he had to give the customer £6 change and he told her as such but next thing he knew she was leaving the store; he told her to wait but she just ignored him and he told me he's been anxious ever since as his till tray is gonna be over by £6.

Please can some retail cashiers or anyone with this sorta knowledge please tell me if there could be troubling consequences for him and I'll let him know. Thank you xxx