I have never tried this, but if you speak about DNA extract stored for more than 3 years without thawing/freeze cycles, I guess you can expect to get 100% of DNA
100% - we routinely store pure DNA (from Quiagen preps, NOT minipreps) in TE at 4°C to avoind freezing/thawing. The oldest ones are for 15 years in the fridge now and > 50% are still ok. I'd say useful lifetime of DNA in TE@4C is around 10 years. Usually degradation is an effect of opening under non-sterile conditions and it is not caused by auto-desctruction!
DNA is ultra-stable! Just think about the Neandertal DNA that was lying around 40000 years in a cave and could still be sequenced :-)
If you want to check on presence, integrity and amplificabillity of your DNA, you can use the PCR-based UBC integrity assay: doi: https://doi.org/10.1101/168195.