My in-game Leaf Ticket display will not increase above 99,999. What happens when I've surpassed that amount of Leaf Tickets in my inventory?

If you have more than 99,999 Leaf Tickets, your in-game Leaf Ticket display will show 99,999+, but the number of Leaf Tickets you possess will be accurately recorded on our servers.
 
Use the following method to check the exact number of Leaf Tickets you possess.
 
From within the game:
❶ Tap the Menu button.
❷ Select Misc.
❸ Select Leaf Ticket Balance.