If Trump loses the election and flees to another country to avoid his sentencing in his (multiple) lawsuits, does the Secret Service have to go with him?

Former U.S. presidents are authorized a security detail from the Secret Service for life. If Trump loses the election and flees the country, does his security detail have to go with him if he requests it?

I imagine this could go down in a variety of ways: He departs the U.S. before he's sentenced and just never returns, or he attempts to flees or does flees the U.S. after his sentencing. Either way, what happens to his security detail?

If he attempts to flees after he's sentenced, I would hope the detail would refuse to take part in it (if he can even board a plane/leave the country to begin with), but given all their failings, who knows.