Fabric backing (linen,cotton and sometimes silk) used to be a normal way to back paper that needed extra support.
In the mid 20th century, Japanese, and Japanese trained conservators introduced the west to Japanese paper backings. Thin paper backings are less intrusive, and the materials more compatable to the paper being backed than fabric.
This new system tended to be used more in North America than Europe, although that has changed in recent years. But, even today French conservators usually back posters with fabric rather than Japanese paper. French conservators are considered old fashioned (to put it mildly) by their European counterparts.
The people who back posters with fabric in North America were either trained in Europe, or got their own training from those following that tradition. I doubt you would find one conservator in North America who has done a fabric paper backing in the last 20 years or more.
Paper behaves differently than fabric, so the two adherends are not very compatible.
Adhesives are a whole different story. Wheat starch paste has a history in the west similar to Japanese paper - not in wide use till the '50's or so. In Europe, fabric backed posters were (are) applied with animal glue, sometime hardened with alum. Alum hardened adhesive are difficult/impossible to remove. Sometimes the adhesive is animal glue and starch paste.
According to one source, the fabric is stapled to a wall or board, and slathered with adhesive. The poster is then brushed on and left to dry. This results in a very stiff, flat poster.
Animal glue backings are messy and time consuming to remove, but not impossible, as long as there's no alum involved.
I've seen posters backed with a Japanese type paper interleaf between the linen and the poster. They said they used starch paste, but it looked "BEVA - y" to me. Or, it could have been some other type of dry mount tissue.
So, reversibility is unknown - sometime yes, sometimes no. There is no one way to apply linen backings, and without a treatment report there is no way to really know what was used.
Rebecca