If the trailer is targeted, yes, they can easily bring a spare. Actually, you probably already have one, unless youíre going to remove that, too. A wheel-less trailer would have the appearance of a derelict vehicle, which might run afoul of local parking ordinances, campground policies, and/or backcountry rangers.
I agree that a campground or a storage lot associated with a campground is your best bet. Public campgrounds generally have rules prohibiting unattended campsites- demand is high, and you are preventing someone else from using the site. Private campgrounds are likely to be more accommodating, and some have storage areas. Thatís where Iíd look.
Security depends on where itís parked, of course. A larger trailer like the Escape
19 is less vulnerable to begin with. A good quality wheel lock that covers the lug nuts is one option. It would deter opportunistic theft, but not a well-prepared thief targeting your trailer. For that or in the backcountry, consider adding a GPS tracking system.