Probably read in the 80s or 90s. USA English paperback.
People from various time periods are living on an island or enclave/settlement on a beach. (Seem to recall a scene were a couple of people were looking out at the ocean while talking)
Story is set far in the future. There was a small group of people from various times (for example someone from 21st century, a couple from 22nd century, some from 24th century, and a couple from 30th century, etc.)
I think there may have been only 25 people total. (pretty sure it was less than 100)
The one from the 21st century had little more than the clothes he was wearing. The others had some of the advanced tech from the times they came from. For example I think the 2 latest (ie 30th century) had self contained habitat/vehicle/ship/craft (spaceflight capable?) that they lived in.
If I recall correctly, one of the ones from the 30th century (Woman I think) always stayed in her habitat. No one had ever seen her.
I Think something happened and wiped out humanity (like in 40th century) and the story is taking place in the 50th century.
I think one of the people from the 30th century had gone around and was finding the last surviving peoples and gathering them at the settlement. (people in time capsules? Suspended animation? Frozen Alive? Stasis Bubbles?) which was why they were all there.
The person who gathered everyone may have been an astronaut who had been on a long exploration voyage (visit another star?) who on return found nothing left of civilization.
The story focused on 2 mysteries:
Trying to piece together what happened between the time of the latest person (30th century) and when the story is set (50th century) to the world so that no one was alive.
Someone is killing the people in the settlement. So they nominate the person from the 21st century to be the "detective" to try to figure out who it is. (I think the reasoning for picking him is he is the most primitive, most active. The others especially the later years are used to having machines do everything for them, i.e. cant think for themselves. Or like some from the 24th century spend all their time taking drugs to keep themselves happy all the time. That's what people in that time period all did.)