Tracfone has plans where minutes won't expire for 90 days, or for a year, depends on how many minutes you buy - https://www.tracfone.com/direct/controller.block. 400 minutes for $99 yields 1 year of service.

Tis the price you gotta pay.

I've carried a Tracfone phone for two years now, for emergencies and urgencies ("They're out of Rocky Road. What flavor do you want?"). I am quite happy with it, since I don't "need" anything but a basic phone.

The $99 worth of time is good for a year, and rolls over when you buy more.

$8 per month is pretty good for a basic phone.

What network(s) does the TracFone run on?

They "use the nation's leading cellular providers to create a national footprint covering 99% of the U.S. population."

Their coverage maps are here.

[Standard disclaimer, I'm not affiliated, etc. etc. :)]

Nextel, and Boost, work on the iDEN network-independent of Sprint. I work for Sprint, so I can ASSURE you there is a network difference.
That being said, as a backup, I would also suggest a PAYG phone-either GSM or iDEN based, as the towers Verizon uses are the same ones Sprint does, and vice versa.