If you buy on eBay, make sure the seller's feedback is 99.6+%. 99.0% is not good. Watch for insane shipping or insurance charges, and keep in mind people might be stupid or lying if their feedback is not good.
"Unlocked" means the phone itself won't argue with you trying to activate it with a carrier other than the one it came from, but it still has to be compatible with whatever system you use. Verizon needs a CDMA phone that does both 800MHz and 1900MHz (not either/or). No GSM phones (including Cingular, T-Mobile, or AT&T) or TDMA (really old system) will work at all, unlocked or not.
Sprint phones have compatible CDMA hardware, but are hardly ever unlocked. Sprint and Verizon are the only major CDMA carriers, so...
You basically need to look for a used Verizon phone. Limited options, but at least it's simple. Trying to find something branded for a less common carrier that will still work will be more complex and unlikely to pay off.
I'm not sure if Verizon is doing this, but they might not let you activate older phones not compatible with their fancy new 911 locator system, so try to get a recent model. CDMA phones do not use SIM cards, so you can't just switch it yourself without Verizon allowing it.
After all that typing, I am thinking you should just call Verizon and see what they can sell you. You don't have as many options as you would with a GSM carrier. If Verizon will sell you a new phone for $50 or less with a contract extension, it is probably not worth the risk of getting a used one on ebay for not much/any less. Unless she want an upper-end phone that is expensive when new.