Does she have to leave the airport and come back in?

Mostly

There are no transit facilities in the US from abroad, all passengers are required to enter the country.

When disembarking as a US airport from abroad, everyone (unless coming from a Precleared airport like in Canada, Dublin or Abu Dhabi) will be forced to go down to border control, like if they were going to exit.

They then collect their checked bags and pass customs. After that, transfer passengers can drop their bags on the carousels.

I don't know if T4 at JFK requires to go through TSA (airport security) again on transfer, but most will just dump you at the exit and you will need to come back in as a departing passenger by passing TSA.

Does she have to leave the airport and come back in?

Mostly, you may have to leave the secure area while transferring (and in some cases have to leave the airport building proper to take a bus or a peoplemover to change terminal), but depending on the exact airport and terminal, it may not happen.

There are no transit facilities in the US from abroad, all passengers are required to enter the country.

When disembarking as a US airport from abroad, everyone (unless coming from a Precleared airport like in Canada, Dublin or Abu Dhabi) will be forced to go down to border control, like if they were going to exit.

They then collect their checked bags and pass customs. After that, transit passengers can drop their bags on the carousels.

I don't know if T4 at JFK requires to go through TSA (airport security) again on transit, but most will just dump you at the exit and you will need to come back in as a departing passenger by passing TSA.