What do you folks do with those empty tubs?

+1 on using for samples. Nice big container to lather soap sample. Easy cleaning when done. Real easy cleaning if used once and sample binned.
5 packs or loose blades
coaster for "beverage" bottle or can
handy-man storing of hardware for Ikea items, swing sets, other projects where reading the directions is optional

They make good holders for (a) paper clips; (b) loose change. I like the idea of using them for new soaps but haven't tried it yet.

+1 on using for samples.  Nice big container to lather soap sample.  Easy cleaning when done.  Real easy cleaning if used once and sample binned.
5 packs or loose blades
coaster for "beverage" bottle or can
handy-man storing of hardware for Ikea items, swing sets,  other projects where reading the directions is optional

I actually use an old Tabula Rasa Steam Punk tub for just that purpose.

Hobby and hardware parts. I'm in the custom RC hobby, and I have LOADS of tiny little parts, screws, washers, nuts, pieces of plastic, and scale accessories laying around. I can;t wait until I polish off a couple tubs of soap to make containers for all these little clips and screws...

They will make excellent holders for standard sized hardware, driver bits, sockets, and all manner of household and automotive parts that always get lost at the bottom of a tool box, as well...

Of course, I also plan on buying refills for many of them when they disappear, so the tubs will simply be rinsed and reused for the same soap...

I've transferred some moisturizer into one so it's easier to just get a bit instead of a large squirt every time. I know there is someone online that 3D prints razor holders that fit in them to protect your razor when travelling.

Send them to me I'll take them

I used to just toss them, but I started saving mine for soap samples or if I decide I want to grate a soap into a bowl (haslinger being a perfect example).

Empty tub? I've never seen one. Does such a beast exist?

Empty tub?  I've never seen one.  Does such a beast exist?

I have actually had two or three... in twelve years of wet shaving.

I do not buy plastic tubs. All plastic is partly virgin material and to various degrees recycled. The problem is what little is recycled eventually becomes product not recycled. The number one particulate material after salt in the world oceans is plastic. Off the US island of Wake all world currents eventually push a large percentile in a floating island once measured as large as Texas. Plastic particulates are now found in the flesh of several species also suffering from mercury poisoning. Plastic fishing nets become floating dead zones of ensnared marine life up to and including turtles and the great whales. smaller species including seabirds will ingest or become trapped in the debri leading to death.
So, ethically I only buy soaps that come in recyclable paper, aluminum or glass.