Shifting the burden of proof means saying it is up to someone else to prove or disprove a claim.
The common internet catchphrase "do your own research" is an example of shifting the burden of proof.
“Two days after getting the jab, a friend of mine’s friend had a heart attack,” a Reddit user wrote recently in a discussion about Covid-19 vaccines. “I’m not saying they’re connected, but D.Y.O.R.”
(Source: NY Times)