Probably not Putin directly, but with Trump's horrible record of debt, multiple bankruptcies and such a filthy record of screwing over people he has had to pay, there is no conventional lending institution which would entertain giving him any money.
Unconventional lending sources, however, may have bailed him out in exchange for favors of one kind or another.
Some Russian oligarch or banking institution may very well fit that description. Trump likely owes some powerful person in Russia a great deal. Putin, who effectively owns (or overtly controls) all major industry in Russia, wants what is best for his own interests.
And, a Trump in the White House seems to be what he wants.
Whatever favors Trump owes his back alley lender will likely be turned into policy changes (or selective enforcement) which will allow Russia to do what they will.
Soon, you'll see the US become extremely lax in NATO as Russia continues to push those boundaries, possibly to the point of war.
Russia will slaughter what's left of the Syrian rebels without repercussion.
Russia will continue to annex former Soviet states.
NATO will be compromised. And, Trump won't do anything about it.