This is maybe a minor tactic but it can be really effective at times. I would be the first to tell you I do not use sunken terrestrials all that often. It is more exciting to catch them on the violent hopper eat or on an ant or beetle that is slowly slipped from the surface, at least for me. I would guess that 90% of the time that I fish sunken terrestrials, it is an ant. There are three methods I have used, 1) it is fished either behind a dry - much like you would fish a nymph dropper, 2) I fish a sunken terrestrial several feet behind a small New Zealand-style yarn indicator like I would a nymph, or 3) I grease the leader with a little floatant to a foot or so in front of the fly and use that as my indicator. The last option is best for flies I want fished just under the film.
To be quite honest, it is probably a method of last resort for me and most fly anglers. I can't imagine many anglers head off to the stream thinking that they are going to spend the day fishing a purposefully submerged terrestrial imitation. More likely, at least for the bulk of us, we give it a try when nothing else is working. Taking it one step further, I will venture a guess that most anglers that fairly commonly fish submerged terrestrials picked up the habitat because they saw their less than dry, dry flies get taken under the water and caught fish that way.
Sunken Imitations
Typically, sunken terrestrials are fished as a just below the film fly but they don't have to be. Look at any fly shop's terrestrial fly offerings or any list of "must have" terrestrial fly patterns and you are not likely to see many non-dry fly options. And what submerged patterns you do see, most of them are ants.
Ants are simple - most imitations are much more more than two bumps with something to imitate legs between those bumps. And without needing to float the fly, submerged / sunken ant patterns will be even simpler. You'll see fur ants, epoxy ants, bead ants, and others but I assume you see few of them in most angler's fly boxes.
I have seen other patterns for fishing sunken hoppers - like The Flopper - but can not say it is something I have experimented all that much with. I have "messed around" with adding a split shot above a hopper and fished them through or downstream of a riffle but it is not something I have done all that often.
This hopper and another version Davie McPhail calls a Claret Irish Hopper, as best I can tell, were created to imitate "duck flies" or their larger chironomids. We tend to think of chironomids as small flies - sizes 18 and smaller - but there are many larger "midges" like those of many western lakes and the "lake flies" of Lake Winnebago are chironomids (or close dipteran relatives). The Kamloops Region of British Columbia, Canada is particularly known of its chironomid hatches and fishing for large trout in lakes. Anyhow, I am sure that these "hoppers" will work just fine to imitate terrestrial hoppers as semi-dry or sunken flies and I plan to give it a try.
I see much less about fishing sunken beetles or crickets - however those Irish hopper flies above would make great cricket imitations. The Coch-y-Bonddu is a historic Welsh fly that is meant to imitate underwater beetles. The name means red and black which refers to the original hackles. Finding the true Coch-y-Bonddu hackle today is nearly impossible so most substitute furnace hackle (also not always so easy to find).
The only more recent fly I can think of that fits the sunken beetle description is a Minnesotan fly, the Black Wet Fly. Dave Anderson (On the Fly Guide Service) credits Tom Dornack with creating the Black Wet Fly. I can't find much information about it or other fly patterns unique to Minnesota. Dave shares that it was created as a sunken beetle imitation and is often fished as a dropper below another terrestrial dry fly.
Sinking (Otherwise) Floating Imitations
The other option is to sink your dry flies. Of course, as you continue to fish them, many flies take in some water and eventually start to float less well. This is particularly true of fur ants and other flies made of natural materials. This works fairly well - accidentally most of the time, I am sure - to fish terrestrial imitations just under the surface film. I have also accidentally found that really small foam ants often lack enough foam to float them, making them, essentially, in-the-film or sunken flies.
Many dries - especially those tied with a fair bit of foam - are really hard to get to sink but you can accomplish it with a little weight on the leader. While certainly a pretty minor technique, it can be accomplished with a bit of split shot, putty weight (do they make that anymore?), or a bead threaded on the leader. I think many dry fly patterns would look pretty sterile, non-lifelike in the water. And I would think that at sunken grasshopper would be a bit more of a mess of wings and legs underwater. So a pattern of natural materials with a distinct wing - like Joe's, Dave's, or Whit hopper along with the Letort hopper and cricket and Gartside's Pheasant Hopper would make better sunken hoppers, I think. They'll probably all work a little better after trout teeth have messed them up a bit more.
Wrap-Up
You are having a rough day and nothing is working - we've all been there. Why not give something different a try? That is how I assume most anglers come to sinking their terrestrial imitations. It is generally a pretty minor technique and one I certainly only toy with on occasion but it is worth keeping the idea in the back of your brain.
Links about Sunken / Sinking Terrestrials
Project Terrestrial Installments
Part 6 - Sunken Terrestrials (this post)
Part 7 - Seasons of the Terrestrial "Bugs" - a terrestrial fly box (coming next)