Can a person be deployed when they have less than a year left when they would return?

Yes, The Army does own you and they can do as it please's.
The way I see it is how much time do yo have left, And how long is the deploment time. As well where do you fit in the needs of your Unit. If you are a 11B in a Infantry unit that is a full strength or is you unit short. The short ansewer is how bad are you needed for the Mission. Regarless of your M.O.S.
Any one can be a Stop loss per need's of your unit.

As long as you wear the uniform until you ETS.

When my Reserve unit was going to be deployed a few years back, I had less than a year left, my unit asked if I wanted to go, and I believe I even signed paperwork acknowledging that I knew how much time I had left, and that I was willing to go on the deployment with them.

As of 2015, some soldiers were being separated prior to the end of their contract if they didn't want to re-enlist or extend, and they were facing deployment https://www.armytimes.com/news/your-army/2015/01/23/policy-will-force-out-enlisteds-slated-to-deploy/.

Sure can

I was in the Air Force and I returned from a deployment with 12 days left on my contract.

Lol of course brother you can actually get deployed (to combat) until past your ETS. This was very common about 10-15 years ago when IRQ and AFG wars were on full blast. But for this to happen stoploss must be in effect.

Check it out, this guys never heard of STOPLOSS.

Yes I currently am in the same situation and just got back from my deployment. You are afforded a 90 day window before ETS to complete SFL-TAP and if you chain of command is gracious enough they will grant your ETS leave in conjunction with it. Although it is not guaranteed, you can be waived to a 10 day period to complete SFL- TAP and sell back your leave after ETS. But like it was said earlier if Major Conflict arises tomorrow you will still be contractually obliged to fulfill those extra years of IRR that came with your original active duty contract.

We got extended 2 weeks on a deployment from Oki. A Marine started his 2 weeks of terminal leave 2 days before we left for home.

To the point yes. Also if stop loss is applied you could be deployed even if you have less than a year prior to deployment