How to exit Singapore after skipping the leg of a flight

Hello, I have a flight booked January 12 from NYC to spend 3 days in Singapore and then the other leg of my flight brings me to New Delhi (I wanted to travel India for two months). There's been 17 deaths in India this weekend because of manifestations and I am supposed to arrive in New Delhi a few days before Republic Day (aka not a good idea to be in the country at that time!!).

The government of my country has issued an alert for travellers going to India but I called the airline and they still are not going to be modifying or cancelling the flight. I was therefore thinking of skipping the last leg of my flight and from Singapore travel to Malaysia by bus. Am I going to have any issue crossing the border? Does it require a special exist stamp or anything like that ? If questionned can I say I got super drunk and missed my connection flight so I decided to not go to India at the end?

N.B. To give more context there is no time constraint as I'll be travelling in Asia for a few months.

Thank you so much!