What happens to the Children

I don't think that the scenario changes regarding the new Stories feature. Meaning, that I do believe that they are put into the Sim's system and are simply gone (though I am not sure if they are able to eventually or randomly able to be adopted through the adoption portal). I recommend having them live with a family member if you want them to stick around controllably. I am curious to see of other's response. 

@candiecoatediv , like @MzMelonz and @valohim666  said, the game simply ends if there are no teens or older in the household.  I just tested it and it gives you the choice to go to the main menu (I guess so you can load a previous save), or something about saving the game and I think that lets you return to the neighborhood to choose another family to play in that save.  But any kids or pets will disappear as if they never existed! 😱😭  In the Sims 2 and Sims 3 the children would be put into the adoption pool so that another Sim could adopt them, but sadly the Sims 4 does not do this! 😓  Before the elder parents die, I would move a freind who is an adult into the household and they can continue to care for any children or pets you have.  🥰

This reminds me of the Sims 3, I always used to befriend Buttercup Rattlebag's owner and then ask him to join the household...but just take the dog! I love that little dog.

The benefit of Sims 4 is that you can edit unplayed/previously played households at any time and use the genetics panel to add adult relatives easily. I often do this anyway when I want to return to a family I'm particularly fond of. I add Aunties, Uncles and then Cousins to the family to branch out but you can do this to add a relative to care for the family too. In gameplay you can then click on the child and chose "adopt as caregiver" if you want to but it's enough that there is an adult there with them.

Blimey, tissues anyone? Snuffle. This is why I play with ageing and death off... and cannot watch Terms of Endearment!!!

What everyone else said! There are mods (MC Command Center does this!) that adopt those children and pets into a different household and pop up a notice in case you want to go get them, but the vanilla game behavior is that if there isn't at least a teen in the house they're culled (deleted).

Thank you everyone for the responses. I think the safest thing is to adopt them into the family so I don’t lose them. My actual heart would break if that happens 😩

@xochiquetzl_xkvn Ah so it was MCCC, thanks for confirming that. I thought it was, but I don't play my PC version enough to actually remember lol.

@simsplayer818 I had a sim die earlier that had become one of my all time favorites, and man I've never felt so awful while playing this game. I was playing a different household, though still a part of the same family, when the phone icon popped up for all 6 sims in that household and I just went "oh no" because I had a bad feeling I knew what it was. To be fair it also sparked thoughts of my dad and uncle who both died of cancer, my dad last year and my uncle not even a month ago. Luckily in regards to the sim I still have backups of her. I mean my current save isn't even where the sim came from, she's a child in an older save though I cheated to age her up and saved her to use in a new save (which became my current save). I also didn't let her die off completely, because now the ghosts of her and Johnny Zest (her husband) are living together with and tormenting their youngest son and his family lol.

@candiecoatediv Yeah if you're worried that the last sim capable of taking care of the child is going to die, definitely take action early and get them into a place where you won't lose them. Since you said you aren't playing that household anymore, maybe move the child into a household you have been playing that way you can keep an eye on them more easily.

@simsplayer818 I looked up Buttercup Rattlebag for a picture but it only said she was a small white dog who hyper and playful.  Do you remember what kind of dog she was? 
I haven't seen Terms of Endearment in a looooong time, but I remember my friend and I bawling! 😭  If you want to avoid crying, don't watch Beaches, Little Women, or read Where the Red Fern Grows! 😭

I have never tried adding relatives to my game in the way you mentioned, but I will have to try that! 💡 That is a good tip! 😄