Magnetic tape is basically rust particles (ferrous oxide, FeO) painted/glued onto a polyvinyl composite backing. They have used vinyl, celluloid, nylon and all manner of backing. Nothing lasts forever. There were four primary backing types; each with its own failing:
1. Paper (which becomes acidic),It was initially introduced by Philips in 1963 under the brand name "Compact Cassette". It was not the first magnetic tape cartridge at that time, but due to their marketing plan it quickly became dominant. Sony pressured the crap out of them to license it for free. It went on to become a popular and most importantly re-recordable, alternative to the LP.
2. Acetate (which becomes brittle),
3. Polyester (which may become sticky) and
4. PVC & plastics (which becomes brittle and/or sticky)
After the debut of the Sony walkman in 1981 , its popularity grew even further with cassette sales finally overtaking those of LPs. Prior to that development Viny had remained in the lead due to the greater sales of singles.
It's a common assumption that early wire recorders "evolved" into tape recorders. On the contrary, tape, wire, and disk magnetic recorders were invented virtually simultaneously. These various formats were developed and promoted by competing companies. After WWII wire recorders died off, and magnetic tape took off. I'll write these up some other time.
Magnetic sound recording tape was first developed by Valdemar Poulsen in the 1890s. He used a solid band of magnetically "hard" steel, and this type of tape continued to be used through the end of the 1930s by some manufacturers. The approach more familiar to us was to use a non-magnetizable carrier such as plastic, coated with "FeO" The German company I. G. Farben improved such coated tapes and introduced them for use with the AEG Magnetophon in the 1930s.
Prior to this in 1888, American scientist Oberlin Smith published an article in the magazine Electrical World. In his article Smith discussed the possibility of permanent magnetic impressions for recording sound and suggested, as a medium, cotton or silk thread, in which steel dust was suspended. He did not create a prototype, so the credit goes to the Germans. Which is fine since they lost WWII and we stole all their scientists. Following World War II, the I. G. Farben process was transferred to England and the United States and further refined. Today cassettes are experiencing a minor re-birth as mix-tape nostalgia sets in.