I sneaked around behind the house of the Battle-Born and found a random passage that said 'To'. I used the glitch to get out of Whiterun and where it usually says something like 'To Skyrim', it only says 'To'. I walked towards it and entered the loading screen, where I could hear sounds in the background, but the game froze. Is this a deleted part of Whiterun?
It's in all probability a mistake.
Toggling collision using
tlc in the in-game console, I checked the location you mentioned, and found the 'random passage':
Going 'through' it, I was also shown a black loading screen (with only the mist or smoke), with the sounds continuing in the background. So we need to look for answers elsewhere.
In the Construction Kit we can check what entity causes this behaviour:
To the right we again can see the House of Clan Battle-Born in Whiterun. The red cylinder shape left of the middle is the entity responsible for the 'Activator' showing up in-game. The green cylinder, and yellow arcade/door in the centre, are part of the entity.
The entity is a Reference, with Reference Editor ID 000351EC.
It refers to a Door named "Passage", with the ID "AutoLoadDoorHiddenMinUse01" (an entity used 5 times in the vanilla base game *).
It has no Teleport data, meaning it leads nowhere - which probably explains why it only shows the word 'To' in-game. Nor does it have any other references or scripts to give us a clue to its purpose.
Its checked flags are 'Hidden', 'Automatic Door', and 'Minimal Use':
According to creationkit.com, the 'Hidden' flag should - not surprisingly - hide the Door in-game.
'Automatic Door' means it acts like a portal, and requires no interaction.
'Minimal Use' makes sure NPC's will try to navigate around it.
I couldn't find any mention of the Reference ID through Google, and a quick skimming of the Unofficial Skyrim Patch changelog doesn't give any results either.
My guess it has no purpose (anymore), and can very well be a left-over from development.
It could also still have something to do with the Civil War changes that a playthrough can bring about (linked to Whiterun being under attack), but that's nothing more than a hunch.