Once the left is in power, they immediately turn out to be right wing? Does it happen in the very second they gain power or only when try to keep it? Is running for the next election even though you're already in power inherently right-wing?
As for left-wingers becoming right-wingers, yes that can and does happen.
For example, at the time the terms left-wing and right-wing were coined, liberal capitalism was understood to be a radical left-wing attack on the traditional feudal hierarchy of kings and priests that had ruled France in the past. A hundred years later and those same capitalists who had built their business empires on the back of liberal and left-wing revolution were either cozying up to the kings they'd once scared, or establishing new kings to replace the ones that got destroyed.
But merely running for office again does not inherently make you right-wing. Nor does engaging in a coup or other forms of power maintenance make you inherently right-wing. It makes you an authoritarian.