Sharing some text from the Mycelium Preservation section of Radical Mycology (page 284):
Sterile Distilled Water
Here, mycelium is placed into small jars or 20-milliliter scintillation tubes that have been filled to their brim with distilled water and sterilized. In the absence of air, nutrients, and minerals, the mycelium will go into a state of suspended animation. These jars can then be sealed and stored at room temperature for years, and potentially decades, without any notable loss in mycelial vigor*. This simple, yet incredibly resilient means for preserving cultures was once commonly used in the mushroom cultivation industry. Unfortunately, it has not been well promoted in recent years.
First the mycelium is cultivated on a nutrified agar plate as normal. Once healthy and contaminant-free growth is seen, a piece of leading edge mycelium is then moved to a petri dish filled with distilled water agar (DWA) using a Plate-to-Plate Transfer. Once the mycelium begins to run on the water agar, several pieces of myceliated DWA are moved to a scintillation tube filled with sterile distilled water in the transfer space. The tube’s lid is then tightly screwed on and a double layer of plastic wrap is applied. The tube is labeled with date and species, then set on a shelf where it will not be disturbed.
* - The reference given here is the following paper:
Richter, D. L. (2008). Revival of saprotrophic and mycorrhizal basidiomycete cultures after 20 years in cold storage in sterile water. Canadian journal of microbiology, 54(8), 595-599.
An updated version of the paper from 2018 (30 years of cold storage) is available here (PDF).
Distilled Water Agar (DWA) Recipe
500 ml distilled water + 10 g agar agar