Is your relative's irresponsibility financial or just forgetfulness/clumsiness?

If it's the former, you're on the right track with prepaid. If you really want to make it easy for them, you can do 3-month, 6-month, or 12-month refills for Straight Talk with some associated savings (strangely, the per-month cost is less for 3-months than 6-months, but 12-months is the cheapest).

If it's the latter, I'd say either go super-cheap on the phone (cheap to replace if lost/stolen) or add an Otter Box or similar rugged case to help prevent breakage. (though doesn't help much with preventing loss). On the low end of phones I'd lean towards the Nokia Lumia 520 or something from Blu if they'd prefer Android. Otherwise, the Moto G, Moto X (if the Today Show $150 discount is still active), or Nexus 5 are tough to beat depending on how much you want to spend.

One last option, if you think Sprint coverage would be adequate, would be Republic Wireless. You get a Moto X for $300 with no contract and plans range from $5 (wifi only) to $40 (unlimited calls/text/LTE data), with a couple of interesting options inbetween ($10/mo for unlimited calls/text but wifi only data, $25/mo for unlimtied calls/text/3G data). The drawbacks CAN be the Sprint network (depending on your location) and the Republic Moto X hasn't received the KitKat update yet. I was about to switch to Republic from ATT, but I switched jobs and my employer just took over my ATT line.