I am also in India. I have similar questions, and did a little searching on this topic, but I doubt there is a well-defined answer. However, I have a few comments to make, and they would be too long to fit into a comment.
First, the term "safety" is relative. A more concrete question to ask is whether it is safer than a savings bank account, or a Fixed Deposit, traditional choices which are still quite popular in India.
Five ways in which debt funds score over fixed deposits (FDs) has a few interesting comments to make about this. Whether these comments are true or not, I do not know, but it does suggest a direction or two to explore. The relevant section from that article is
Unlike debt funds, the risk of concentration is high in investments
like fixed deposits where investors hold large sums of money and run
the risk of losing it all if things go wrong. There is very little
information available to investors that they can use to evaluate their
investments and they have very few options for exit or redressal.
Open-ended funds, on the other hand, are required to provide regular
information on portfolio and performance to investors and can exit at
the current value of the units at any time.
It is definitely true that in India, bank accounts (unlike in the US or the EU) are not safe, because the deposit insurance amount, till recently 1 lakh, and now apparently 5 lakhs, is grossly inadequate. And apparently (I am not completely sure of it), that amount is only paid once the bank is liquidated.
The Indian cooperative bank sector is a good example of banks where failure is not theoretical. Indian cooperative banks fail all the time, yet the govt allows them to run, and no notification of this is given to depositors. The recent PMC bank collapse was possibly the most recent, and probably the largest. And the depositors still have not received their money after more than 6 months. But are even big banks completely safe, if the insurance amount is so meagre.
I thought that article's comment that "Open-ended funds, on the other hand, are required to provide regular information on portfolio and performance to investors". Is having information about portfolio helpful in helping depositors assess risk?
There is the very recent example of the Franklin Templeton, where to quote from
[Franklin Templeton MF committed to return investors money: Sanjay Sapre]
The asset manager shut down its six schemes Franklin India Low
Duration Fund, Franklin India Dynamic Accrual Fund, Franklin India
Credit Risk Fund, Franklin India Short Term Income Plan, Franklin
India Ultra Short Bond Fund and Franklin India Income Opportunities
Fund on Thursday. The six debt schemes had assets under management of
over Rs 25,000 crore.
So it's certainly possible for things to go bad, but could this disaster have been forecast from knowing those fund portfolios? I don't know the answer to that, but if I discover it, I'll update this answer.
And it's true that savings bank account and FDs are completely opaque. You basically have to hope that the bank does not run into trouble, and that if is does, it gets bailed out, as happened to Yes Bank recently.
The RBI does have a Too Big to Fail criteria, which apparently currently includes SBI, HDFC, and ICICI. Which means that it will (probably) bail out those banks, because their failure would cause systemic problems. But it would be nice not to have to rely on something like that.
Finally, it's worth noting that overnight funds are supposedly the safest of the debt funds, because their portfolio is based on financial instruments that mature overnight. These are slightly safer than liquid funds, which are typically based on instruments that mature in less than 90 days. Overnight funds should be considered direct competitors to FDs, because their yield and taxation rate is very similar.
I'm not aware of any overnight funds which have run into trouble. Of course, that does not mean there have not been any. If you are aware of any such happening, please update the question. I'm also unclear how long overnight funds have existed in India. I found some mentions which seemed to suggest that they first got their current labelling by SEBI in 2017-2018, but it's hard to imagine they did not exist earlier.