If the shareholder is eligible for the rights issue, their demat account will be credited with right entitlements (REs). REs can be used to apply for the rights issue or can be transferred by selling them on the market. If they are not sold or used for applying for the rights issue, they will eventually lapse.
If the RE has been purchased, you will also lose the amount paid to acquire those REs. Thus REs in themselves do not mean you hold rights shares. The rights shares need to be applied for by the issue closing date. As per the SEBI mandate, if you neither subscribe (apply) for rights shares or sell the REs in the secondary market, these rights will be extinguished after the closing date.
To know more about Rights Issue, get the SEBI FAQs here, NSE FAQs here and BSE FAQs here.