If this has been discussed before, I'm sorry that I cannot find it. However, this has happened to me on three separate occasions, and since I know that it causes real problems, I thought I should share.
I have played with imaginary friends, even growing up and marrying them, without any problems. The problem only appears when there is more than one imaginary friend doll in the household (even still in the mailbox!). When there is more than one, the game lags to the point of stopping, and if ignored, it will start causing saving issues.
My "evidence" is experience. In first experience, I'd been playing the family for a while and had twins who both received dolls. I'd had these dolls in the household before, but never more than one at a time. When the game started stalling and then threw the dreaded Error Code 12, I tried many things to save it. One thing was cleaning up personal inventories, and since I had no desire to grow up the two dolls, I deleted them. The problems went away, but I wasn't positive that the dolls were the cause.
The second time it happened, I was much more certain. In that family's second generation, twins were given the dolls. All was fine for a couple of days, but lag was getting worse. In my efforts to resolve what could be happening, I remembered my first experience with multiple dolls. So, I confirmed the lag problem was still there, deleted the dolls only, and the lag disappeared.
Last night was the third. I have a family on generation 9; they had a set of twins who both received the dolls, and I deleted them. Then they had another set of twins early Tuesday morning. By the end of Tuesday, lag had increased a lot, but Mom needed to take a trip, so I just whisked her away instead of thinking much about it. The game was fine on vacation and saved properly before return, but when Mom tried to return to town, Error Code 12 popped up. I loaded my pre-vacation file, noticing that Overwatch showed a couple of sim errors but not paying a lot of attention. The game was practically at a stand-still and then crashed. I re-loaded the game figuring I would have to move the family to save them, but this time I realized that the sim errors were popping for imaginary friend names. /facepalm Sent someone to the mailbox, and there they were, the new imaginary friend dolls. Deleted them immediately, and all lag disappeared.
For the record, I have all expansions, lots of store items, come custom content, and a few NRaas mods. All of the content and mods were not necessarily present for all experiences. Also, I play on my desktop as well as my laptop, so the experiences span different machines with different capabilities.
I sure hope this helps someone save their game without going through the frustration of trying to figure out what's suddenly causing the problems. :-)