Are you in the right forum? AACW doesn't have stockades; CW2 does. CW2 questions should be posted here: CW2 Public Forum
But anyway, to answer your question, when dealing with capturing regions without garrisons
, and their content, the most important factor is loyalty to your faction.
If you have >50% loyalty, and you send a Partisan not in PP (Passive Posture - stacks in PP generally have no affect on the game) into a region with a city, and any other structures, that unit will capture the city and any other structures in the city. You will simply gain control over them.
If you have =<50% loyalty in the region, and your unit ends its turn in the region, whether that stack still has movement plotted at the beginning of the next turn or not, you will not capture the region and it's structures, BUT if the city has any supplies, you will take some of those supplies and destroy the rest, and if there is a depot, your unit will destroy the depot, and if there are other structures like factories, there is some chance that one or more of these will also be destroyed.
I'm not exactly sure about purposefully destroying a depot you control, with regards to the time. I think the 5 day minimum was removed, but I think it now works about the same as damaging rail lines. You have a percentage chance of destroying the depot compared to the stack's strength (Partisans get +25% IIRC). So if your Partisan unit has lets say a strength of 15 +25 for being a Pillager, you would have had a 40% chance of destroying the depot in Rolla if you had given the Partisan unit the Destroy Depot SO (Special Order) and plotted it to leave the region, or stayed for that matter. If you really wanted to be certain, put the the Partisan inside the city, set it to Hold at all Costs, and give it the Destroy Depot SO. This would give you the best chance. Unless the attacking brigade is set to Assault, it will not attack your Partisan inside the city, which will give you a second turn to try to destroy the depot, if it didn't work the first time. Even if they were set to Assault, your Partisan might survive the Assault and still have a small chance on the next turn, but better than nothing.
With Stockades, it works pretty much the same, except that Stockades have auto-garrison, which means the even if you do have >50% loyalty, there is about a 50-75% chance that a garrison will spawn when your Partisans enter the region, which will prevent you from automatically capturing the Stockade. Of course, if it doesn't spawn, you will capture it, even if you are simply passing through the region.