You don't get a free flight. Typically either your return ticket is moved if possible, or the airline will claim the cost from you. There's a number of regulations and airline rules, but in general - unless the airline messed up checks at boarding, you're getting charged for the flight back.
This page[1] says "The majority of removals are carried out by air at U.S. government expense." which sounds like a free flight to me. Looking at prices, a near term one-way, no stops flight is about $500. There's some expensive days, and if you wait two weeks, you can save about $70 on the flight ... doesn't seem to be worth the wait, assuming detention costs are more than $5/day. But I'd say waiting a few days to avoid some of the $1000+ flights would make sense.
Generally I'd expect a deportation process to take quite some time because immigration courts have not been properly staffed. But I would have expected ICE to offer either a withdrawal of application, or voluntary deportation, both of which involve travel arrangements at the alien's expense in order to expedite removal. I think it's probably in the person's better interest to pay for a ticket home (hopefully with some credit for their previously scheduled flight) if they were planning on returning home anyway; better to go home early than sit out your trip in immigration detention.
Sounds like she was surviving doing chores in exchange for a place to sleep (in two different countries). It's possible she didn't have a plane ticket lined up.
It's so expensive to not take a return ticket, I doubt she didn't had a return plane ticket. Maybe she moved her flight or missed it, but only rich people don't buy a return ticket.
I am not sure if the comment is serious or not. Often one way tix are not much more than half a round trip tix It used to be one way tickets were like 70+% of a round trip, not as much anymore
