A family member or friend can absolutely pick someone up on their release date. There is no requirement to use the bus or train ticket that the facility provides. The ticket is an option, not a mandate, and it exists specifically for people who have nobody coming to get them or no other way to get home.
When an inmate is released, the facility typically provides gate money, a small amount of cash, and a bus or train ticket to their approved release destination if nobody is arranging transportation. That is the fallback for people without outside support, not a rule that everyone has to follow.
If you plan to pick someone up, it is worth coordinating the details in advance. Find out the exact release time and location, because some facilities process releases at a specific gate or through a separate discharge area rather than the main entrance. Release times can also shift depending on paperwork processing, so building some flexibility into your schedule avoids a long wait in a parking lot.
Confirm the plan with your person before release day so they know not to accept the bus ticket. Once that ticket is issued and used, the facility has fulfilled its transportation obligation and the logistics become more complicated to unwind. A simple heads up that someone is coming eliminates that issue entirely.
Picking someone up on release day is one of the most meaningful things you can do. That first ride home matters more than most people realize.