Will he be replaced next day or is he lost forever? (including the loss of 1 hearthling “slot”)
Short answer: Hearthling (and “slot”) is gone, but might be replaced the next day.
That particular Hearthling is gone forever when he/she dies, except for a tombstone you can remember them by.
When the Daily Report comes the next day, it decides whether or not to give you a new Hearthling based on numbers. Those numbers are determined by how many Hearthlings you have when the report happens. So, if you had 8 Hearthlings, and one died, then your next Daily Report would have the same requirements that it did when you had 7 Hearthlings. If you had 10 Hearthlings, and three died, the next report would still have the same requirements.
Currently, I believe it’s extremely unlikely for you to replace a hearthling right after someone dies. There’s a morale penalty for a while after the death, so when the next Daily Update (or the next couple of Updates) comes around, the morale requirement isn’t high enough for a new immigrant.
This might change in the future, where having a larger population and more influences on morale could negate the deduction’s impact.
I never personally have an issue with morale, even after a Hearthling dies. (My food is always 9.5 or higher, and shelter at the current-max of 5). However, the more Hearthlings you lose, the more likely it is that, as @Atralane says, you won’t get them replaced.
All in all, nothing to worry about. It’s kinda easy to get back meeting the requirements again.
so heathlings compensate their loss by piling up food and wealth? - sounds wrong, if you ask me!
“Hey Karl died last night during a fight with a goblin” … " we should build another storage, iam feeling hungry"