Hi. As a long time player and having tested a lot of stuff related to that issue, it's not related to the TOOL mod only. In an unmodded game also, it's any object you place outside your lot, like for example if you have a keyboard or an easel and you decide it to place it in the world (using the interaction to do so from your inventory), and you load a residential rental, the object is gone.
From what I know, having TOOL installed will prevent objects from disappearing, as TwistedMexi included a fix in TOOL to prevent that (I wish it was available as a standalone for players who don't want TOOL in their games). But in an ideal situation, no fix would be needed.
The original issue where all of that was discussed is here. At some point, there was a new issue added on the top of that that caused all those objects in the world (placed trough regular gameplay or TOOL) to be cloned and this clone to be un-selectable and un-deletable. To solve this issue, they made it so those objects were not visible anymore, but still bloating up save files.
There seems to be a lot of stuff managed strangely with residential rental lots, for exemple, how inventoried objects such as books or toys are handled. Something in this whole system is messing things up, I don't know if that's connected, but it's an issues that should be explored in depth.
