The textbook case is buying credit protection on a company from a bank heavily exposed to that same company. If the company defaults, the protection becomes valuable and the bank is simultaneously weakened, which is what happened to monoline insurers and to AIG's structured credit book in 2008.
Specific wrong-way risk comes from a direct link, such as collateral consisting of the counterparty's own securities. General wrong-way risk comes from shared macro drivers, for example hedging emerging market currency exposure with a bank domiciled in that country.
The controls are structural rather than statistical: prohibit correlated collateral, set concentration limits per counterparty, and stress-test exposures jointly with counterparty credit rather than separately. See counterparty-risk.
Related: counterparty-risk, collateral, credit-default-swap, concentration-risk, central-counterparty, tail-risk