Rexine is a material used widely as a substitute of leather. However, there is not much clarity on the materials used in its production. Sometimes, it is even referred to as "Artificial Leather". Does the production of raxine involve killing animals?
Rexine and other artificial leathers are cloth-backed plastics
In general, the whole point of artificial leathers is to not be animal skins, for either ethical or cost reasons. The cloth component is generally plant-derived (again for cost reasons), and modern plastics are purely synthetic.
If that's all you're worried about — that rexine might actually be animal skin — then you needn't worry about that. It's definitely not animal skin.
The Devil's in the details
However, every artificial leather uses its own production formula, and it's theoretically possible that minor chemical additives have an animal source.
Unfortunately, if all you know is that the material you're thinking of is called “rexine”, there's no way to know for certain, since that's not enough information to know what the material actually is and track down its production formula. Brand-name Rexine is a specific type of artificial leather produced by Rexine LTD of the United Kingdom, but much like “kleenex” in the United States, the brand name “Rexine” has suffered from brand genericisation, and now many different materials are popularly called “rexine”.
Brand-name Rexine: probably vegan
Based on Wikipedia's record of the formula, actual brand-name Rexine is probably produced without animal products: it's made from nitrocellulose (which is itself made from cellulose and laboratory-produced, mineral-sourced nitric acid), camphor oil, pigment and alcohol.
The “probably” is because of the non-specific use of “pigment”: the vast majority of industrial processes use synthetic pigments rather than naturally-derived ones, due to greater colour-fastness and lower cost, but since animal-sourced pigments do exist, it's possible — however unlikely — that some colours of Rexine are coloured with an animal-derived pigment.
Buyer beware, and do more research
For all other artificial leathers, the specific manufacturer must be identified, and this can't be done just by finding out what trade name the material goes under. To find out exactly what a specific artificial leather is made out of, you'll have to contact the manufacturer directly and inquire about their formula's sources.
Artificial leathers are definitely not animal skin, and at that “large scale”, they're not animal products.
It's highly likely that any given artificial leather brand does not contain any animal-derived ingredients. For many artificial leather brands, this is the entire purpose. However, it's possible that a given artificial leather brand might use some innocuous chemical as part of its plastic production, which might have some animal source somewhere in its own production history. This is unlikely, but a possibility. If 100% vegan artificial leather is the goal, then the only way to be sure is to talk to the manufacturer of the specific artificial leather and get their response on how they source all ingredients for their formula.
Rexine sounds like a great alternative to leather, not only avoiding animal skin altogether but also being natural, avoiding oil based (basically plastic style) fabric.
A lot of the make-up is cellulose, which is plant fibre. This though might bring us to a situation similar to viscose which is made from plant and wood fibres, but where some have been concerned about chemicals used in in the manufacturing process. The raw material itself is natural and of course causes no animal deaths. However chemicals used might harm the environment (including wildlife) and might further introduce some element of toxicity in usage.
However there's a further negative point to the historical rexine which has me drop the possibility of it being useful altogether. The finish of cellulose nitrate is extremely flammable and therefore quite a dangerous fabric to use, having the potential to enable a small flame or burn to spread very rapidly.
This refers to the original, trademarked rexine, which I doubt is actually made anymore, though might still be made on demand by some producers.
I think that most modern leathercloth fabrics today which are called rexine are not the cellulose based, trademarked original and are likely to be more typical faux leather. (In other words, back to the world of plastics).
The only other natural, faux leather which I have come across is cracked cotton (or chapped cotton), which looks great and works very well. I'm not sure what the issues there about chemicals may be, but in any event it's a very hard to find cloth which unfortunately doesn't seem to be used much.