The cells support the synapses that hold the memory. The cell lives as long as the memory does.
If I understand what is going on in the hippocampus, it holds a mirror of the cortex areas that it is connected to.
During the day the new learning in the hippocampus is the delta between the active recall is in the cortex and the surprise in perception.
The hippocampus is tuned for rapid one-shot learning but this high degree of plasticity has a limited capacity - tunes by evolution to one day.
The rest of the cortex learns more slowly with “normal” Hebbian learning. Obviously- with much higher capacity.
During sleep spindles both areas are interrogated and the cortex is prompted to learn the difference - the new memories.
When both areas respond equally the memories have been transferred.
I see the hippocampus as evolved from the point before sight and hearing- when all the critter had was taste and touch. The chemical signature of the meal (olfaction) was retained until the gut could make the call if it was good or bad. This could be considered the first emotion.
The hippocampus is a vastly enhanced version of this. Sequences are held, along with the emotional values experienced during these episodes. You don’t know if it was good or bad until it is over. What is transferred to cortex is what happened and how you felt about it.