Although there is no verse in the Bible which directly says that the Lord will not destroy the righteous with the wicked, it is assumed that is the case because of the Lord's nature of love, goodness and justice.
Many Christians believe that the Great Tribulation comes from the Lord and so they believe that, in His goodness, He will rapture believers before pouring out His wrath on the earth.
Such belief comes from a lack of understanding of the prophecies and the nature of the Law Of The Lord.
The prophetic verses related to the Great Tribulation use the phrase 'then shall be' and not the phrase 'the Lord shall send'.
When we look at the Four Horsemen of Revelation we must understand that these horsemen are men or aggregates of mankind who through rebellion against the Word Of The Lord bring about conquest, war, famine and death.
These are acts of men and not of the Lord though they are the result of rebellion against the Lord.
When the Law Of The Lord is broken there are evil consequences just as when the Law Of The Lord is observed there are consequences of blessing.
Because our Lord is just and good He could never punish the Righteous With The Wicked.