I live in zone 8B, Salem, OR. My alstroemerias is in a pot and the foliage (no flowers now) is still blooming. Do I cut that foliage? Can I leave it out during the winter under a deck?

Do you know what kind of Alstroemeria you have? In your area, your Alstroemeria (no matter the type) will most likely stay green all winter. Never 'cut' Alstroemeria, rather 'pull' the stems. They will break off at the rhizome and encourage more growth.

If you plant your Alstroemeria in the ground, it will quickly fill up any area its in.

Down here, they die back in the heat of summer, and come back in the fall no matter how much water they get, so I would think yours can make it. Mine are all in the ground. Don't know how they will take a freeze though. I agree that you should never cut them. A pull with a twist is the best way. If you're taking them for cut flowers, cut the stems as you put them in the vase.

I grew tons of Alstroemeria in CA Zone 8 and I have a couple here in Zone 6. They seem to take a lot more cold then might be expected. All my neighbors in Zone 8 had Alstroemeria but I may be unique in Reno.