Most clients (qTox, µTox, Toxygen, Antox, and others) implement pseudo-offline messaging. Pseudo-offline messaging essentially schedules a message to be sent to a friend the next time you are both online. While this can be convenient at times, it still requires both clients to be online at the same time for one to message the other. Fully offline, asynchronous messages would not carry this requirement.
Pseudo-offline messages work similarly to the "Pounce" feature some people may be familiar with from Pidgin. More about Pounce.
Some people have reported setting up computers they trust to relay messages to them when they are offline, often using single-board computers and Ratox or ToxBot to set up the relay. It is up to you to decide if these are appropriate for your needs. Each of them have their own risks and benefits.
Some of the Multiple Devices proposals can also help users either simulate or achieve partial offline messaging. The multiple devices proposals can be found here.