What happens if you convert a 100GB E3 mailbox to 2GB F1 mailbox?

I agree with Juan! 

In fact, it may not work at all and you'll have to reduce the mailbox size to under 2GB beforehand. I'm getting this from https://products.office.com/en-gb/exchange/microsoft-exchange-licensing-faq-email-for-business, though it's not an exact match:

Here is Microsoft's advice to "https://docs.microsoft.com/en-us/office365/admin/subscriptions-and-billing/back-up-data-before-switching-plans" including how to back up the data accordingly.