Note that EMIs are obligated via regulation to keep 100% of their customers' money in zero-risk accounts (e.g. an interest bearing bank savings account). Unlike banks, EMIs can't use that money to lend, leverage, provide credit, or make risky investments. So, in theory, if regulations are followed (and for the majority they are certainly followed) your money is very safe.
A doomsday scenario would be a collapse of one or more of the banks providing accounts to the EMI. As in, a backbone failure. It's an unlikely scenario, and they certainly try to mitigate those risks by working with several large providers.
Then there's the risk of the EMI deciding that they don't want you as a customer anymore. This can happen with any financial institution, and they will not keep your money if this happens, unless instructed to by law/tax agencies.
Does it make it safe?
At my opinion no .
There will be bankruptcy with emi's , it's after all private companies.
And then ....you will not find your money in any segregated bank account.
I use emi's like layers... Not like safe box