In the struggle,the strap broke and,with the bag in their possession,both men started running through the trees.
也就是说 In the struggle,A and B,主句（主语+谓语）
一句句子只能有一个谓语.
“both men started running through the trees”是真正的主句.started是真正的谓语.
“the strap broke” 和 “with the bag in their possession”是同位语.
如果the strap was broken..那么这句句子是错误的.两句句子既没有连词.又没有句号或分号.是个大错误.这里的“and”不是连词.