I don't understand the function of participles in these sentences below.
1- She fled with her children, ending up in a shelter. (Does the action of the main clause( "fleeing") happen at the same the as the action of participle clause? ( "ending up") )
2- Cooper enjoyed dinner at Audrey's house, agreeing to a large slice of cherry pie even though he was full to the point of bursting. (Does the action of the main clause( "enjoying") happen at the same the as the action of participle clause? ( "agreeing"))
3- Three man tried to mug me but I fought them off, injuring two of them. (Again does the action of main clause( "fighting off" ) happen at the same time as the action of participle clause? ("injuring" ))
4- Anthropologists found parasite eggs in ancient poop samples, providing a glimpse of human health as hunter gatherers transitioned to settlements. (Scientific American) (Is this a reduced relative clause which qualifies the whole independent clause? As: Anthropologists found parasite eggs in ancient poop samples, which provides a glimpse of human health as hunter gatherers transitioned to settlements. Christopher Intagliata reports ("which provides..." refers to the whole independent clause" " Anthropologists found parasite eggs in ancient poop samples" )