Suppose we have 1 firm and the firm has three options:
(1) Produce and get \$100 in revenue - \$200 in costs = -\$100 in profit.
(2) Temporarily shut down and pay fixed costs = -\$50 in profit.
(3) Permanently shut down and pay nothing = \$0 in profit.
We think about "producer surplus" in terms of profit or loss (with a discrepancy for fixed costs). So if the firm picked option (3) they would lose $0. But producer surplus is supposed to be a net concept that looks at benefits versus costs. So shouldn't we consider option (2) an opportunity cost of option (3)? It is the "next best alternative". So in a way, you can say that the "producer surplus" of choosing (3) is a positive \$50. Does this make sense?
A similar thought experiment would be if we had two firms with the same options as above. Firm 1 picked option (3) and firm 2 picked option (2). What is the difference in their "producer surplus"? Is it \$50, by comparing profit or loss, or is it \$100, by comparing this "new" producer surplus? When would the latter make sense?