In the later levels of the game there are raids from flying creatures. These flying creatures will attack and kill your tamed creatures unless they are in a roofed enclosure.
You'll want to build a roofed barn to hold your tamed creatures and its also best if you put a fence of some kind around that barn because adult creatures can clip through the walls when you are loading into the area and this will result in them being outside the barn. (Its even better if your barn with fenced in yard is inside defensive walls or a compound that you have built for other activities (like sleeping, resting, gardening, and smelting.)
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I bet Boris just wanted to settle in a different place. He knew you would find him and build new pen around that better location.

If the distance is too much for you to bear
Once fenced in, you can take your time with a corridor along which you can easily push him but like Brakxel said; but this is only good for short distances.

One thing about how-to not lose all your herd in a raid/to random grounded enemy:
Build secondary but somewhat bigger perimeter around the pen. For example I have few meters between these defensive lines and the mobs don't notice the herd nor is the herd alerted by a wondering mob so nobody aggros at nobody and usually nothing attacks the fence.

Originally posted by sneakyweazel:

One thing about how-to not lose all your herd in a raid/to random grounded enemy:
Build secondary but somewhat bigger perimeter around the pen. For example I have few meters between these defensive lines and the mobs don't notice the herd nor is the herd alerted by a wondering mob so nobody aggros at nobody and usually nothing attacks the fence.

This is good advice. That's how my first pen of boars got free. A mob wandered by and spooked the boars. The boars busted down the little pole fence. I come home to boars in the kitchen. The outer perimeter fence was built the next day. Corralled who I could and made sausages out of the others.

"made sausages out of the others" <shudders>

You can push boars by walking into them while they stand still, but this is only good for short distances. You can build a pole fence around him and "guide" him back home. Fence a narrow path back with food along the way, but again distance and patience is at play here.
There is a harpoon you can get later, but it does damage and not sure how well it work. Never used it.
I use a mod, Valheim Plus, and an option is to make your tamed pets invulnerable to everything but your meat cleaver. I use that now and when my pigs got out they were very helpful in raids and clearing wandering mobs. Nothing can kill them so they run interference. Very satisfying having a pack of watch pigs take on a skeleton invasion.
You could do something like that and know where ever Boris goes he will be safe.

If you want to move your tames you'll want to use a harpoon (while enabling PVP in order to use it on them) or push them yourself, which isn't really that great of an idea over a longer distance.