President Abraham Lincoln did not offer any compensation to the Border States in exchange for passing laws to abolish slavery over time. Lincoln was opposed to slavery and believed it was a moral wrong, but he also believed that it was important to preserve the Union and prevent the country from being torn apart by civil war.
Lincoln's approach to abolishing slavery was focused on using his executive powers as President to gradually undermine and ultimately eliminate the institution. He issued the Emancipation Proclamation in 1863, which declared that all slaves in the Confederate states were to be considered free. This did not immediately end slavery in the United States, as it only applied to the states that were in rebellion against the Union. However, it was a significant step towards abolition and helped to set the stage for the 13th Amendment to the Constitution, which was ratified in 1865 and officially ended slavery in the United States.
The Border States were slave states that remained loyal to the Union during the Civil War. Lincoln did not offer them any compensation in exchange for abolishing slavery, but he did offer them incentives to remain in the Union and support the federal government's efforts to end slavery. For example, he offered to compensate slave owners for their loss of property if they agreed to free their slaves. However, this offer was not widely accepted and had little impact on the overall course of the war or the abolition of slavery.