You can't change the way they were stored now, so you have only two options, select a couple of samples and try extractions (you can test the RNA quality after extraction) or discard the whole batch of samples. If you think that worth the try then you can also try to add RNA stabilization reagent by yourself to the frozen saliva sample, cap the vial and let sample thaw on ice inverting sometimes the vial. This will probably ensure a minimal RNAse activity in the meantime of RNA stabilization reagent diffusion into thawing saliva sample. 

Thanks for your suggestion, Paolo. Since this batch of samples is retrieved from a cancer patient specimen archive, and it is not able to recollect the samples. Therefore, I need to try everything feasible to do the extraction. I am going to try your method. Did you try this before?

Unfortunately I never tried this specifically on saliva specimens but actually seems the only way to improve the yield of good-quality RNA. RNAses are strongly active at room temperature but the activity is negligible around 4 degrees and almost absent at -20. You should unfreeze samples for exctraction, thawing on ice require more time rather than room temp thawing but it is better for quality preservation. As soon as the frozen saliva become liquid it can mixed with RNAses inhibitors already added reducing endogenous RNAse activity. I guess it's also better to extract RNAs immediately after thawing and hold them as less as possible at room temp until they're reverse transcribed.

It is true that saliva is a huge bank of enzymes, however, no enzyme would be working at minus 80 degrees. So, as far as you let your RNA specimen to thaw on ice and then add the RNA stabilizers according to your SOP, you should be on the safe side regarding your manouevre. The stability issues come into the light  from the moment the the saliva has been collected. and stored. If there has been a huge lag of time between collection and storage, you can look at poor harvest.