Some foreigners living in India may receive a Permanent Account Number card.
Is the PAN number on a Permanent Account Number card a sensitive piece of information?
A PAN number is a sensitive piece of information. It is very much like a SSN given in the USA or SIN given in Canada. All your income is tied to your PAN number. The PAN card can be used as an identity proof in some cases. Many financial transactions like buying mutual funds, gold, stocks, etc. require your PAN information.
There are a lot of tax evasion scams going on in India to shelter black money. These people can potentially use one's PAN information to make transactions under your name and you won't find out till the Income Tax department comes after you. There is a chance one might still be able to prove their innocence. However it is a hassle no one wants to go through.
A lot of this is being changed by the government lately to link PAN information with the new Adhar card which is a whole beast of its own and off topic for this question. You can find more information about it here
I found some information on Quora about where its okay to give your PAN information and What are the importance of a Permanent Account Number?
Here is some info I found about how your PAN card number can be misused. Hope you find this helpful.