What rules have been written for 5e D&D on Failing Forward?

I am looking for the rules in various 5e D&D books for allowing characters to add 1 or 2 points to their die-roll when they roll slightly too low. Searching Stack Exchange i found this, quoted from pg. 58 of the basic rules:

If the total equals or exceeds the DC, the ability check is a success—the creature overcomes the challenge at hand. Otherwise, it’s a failure, which means the character or monster makes no progress toward the objective or makes progress combined with a setback determined by the DM.

1. I could have sworn i found similar rules to the listed / above in the DMs guide years ago – cannot now. Sorry.

2. Unearthed Arcana may have new and brilliant quasi-rules on this. Cannot find it now.

3. Probably discussed already elsewhere on Stack Exchange. If so, please direct me there.

Where are the rules that allow a DM in 5e D&D to add a point or two on a failed d20 role (combat or not). Any rules. A tweet from His Royal Highness Crawford himself would be grand. It is also called ‘Success At A Cost’… perhaps.