Your's may be too far gone, but mine was pretty ratty, drooping and badly discolored, but not ripped. I wiped it down thoroughly with alcohol, VERY carefully tucked the drooping edges back where they belong. Then I removed everything installed through the headliner, isolated it from the rest of the interior with acres of plastic, newpaper curtains and masking tape and sprayed it with three thin coats of white vinyl paint (Duplicolor brand I think). I was prepared to rip it out and install a new one if it didn't work, but the results were amazing and gave the old interior a completely new look with four hours work and about $25. A year or so later no peeling or other issues, looks like new.

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1983 CD
1958 Studebaker Packard (being resuscitated)