REASONS FOR NON-TRADING OF SHARES

1. If your shares are not trading at present, it could be due to non-compliance of any of Sebi's listing rules, when one has to wait for relisting or avail off-market services on offer for sale.
2. If that's not the case, companies may have delisted on their own, when one has to approach them directly.
3. It could also be that they have merged with another entity, listed or unlisted, when the existing entity needs to be approached.
4. In the worst scenario, they may have wound up their operations, purposely or due to bankruptcy, when one has to stake claims, with least priority as a creditor, being an owner of the company to the extent of the shareholding, and which may come to nought too even after all legal hassles.
5. While physical or demat shares do give you ownership rights, only on the company per se, exercising or relinquishing them often becomes a personal choice for a variety of individual reasons.
6. A tip - Don't demat such old "sticky" shares, even if it is possible, till their final outcome is forthcoming, to avoid recurring demat charges on them too.