You want the absolute cheapest for very minimal use?
Lycamobile: 2c/min, 4c/text, 6c/MB
http://www.lycamobile.us/en/national-plans
$10 PIN is good for 90 days.
It's T-Mobile based, so make sure she has coverage.
Also T-Mobile based, the second cheapest option:
Platinumtel: 5c/min, 2c/text, 10c/MB
http://www.platinumtel.com/plans
$10 PIN is good for 60 days.
Lycamobile is very new (although popular in UK and Europe, I believe), Platinumtel is a well known MVNO that used to be CDMA (Sprint) based but just switched to GSM (T-Mobile) back in December.
I just wanted to add that if T-Mobile coverage is unacceptable and AT&T is good, look at the minutes plans at H2O wireless (
https://www.h2owirelessnow.com) or AirVoice (
https://www.airvoicewireless.com/). They both have $10/month plan with reasonable rates.
For super low usage as you said, my suggestion is to NOT pay any amount of big money up front for a year as mentioned above. It's just going to be wasted. Pick a plan with a tight 1-3 month period with no more than $10/month. I think it's much better this way.