What shall we say, then? Shall we go on sinning so that grace may increase? By no means! We are those who have died to sin; how can we live in it any longer?
Romans 6:1-2, NIV
A simple answer to the question about sinning after we are saved, is, yes, we can and do sin, once we are secure in Christ. There apparently were those who believed in deliberatly sinning to increase grace. Perhaps that is who Paul refers to.
It can be very useful to examine the objections to a doctrine such as the Security of the Believer. Perhaps the biggest objection is that those who learn you are saved forever will feel they now are free to sin because there is no loss of salvation. And some do.
But loss of salvation is not the only thing to be considered. Imagine a child who said, "Now that I'm born and can't be unborn, I can be as bad as I want." Mother and Father will have something to say about that. And a good child will want to please his parents out of love for them.
I really believe there is in us the fear that if we do bad we will be lost. This despite our knowledge that the Bible teaches otherwise. Since we are not saved by "being good", does it make any sense that we can lose our salvation by "being bad"? We are trapped by the false idea, promulgated by those who would try to control us by Fear and Guilt.
So what if we go ahead and sin abundantly? Are there serious consequences? Certainly. Disrupted fellowship with God, loss of heavenly reward, and in extreme cases an early death.
Thankfully the Holy Spirit helps us by turning our thoughts and desires away from sin. Though we are free from loss of salvation, we wish to please the God who gave us this security.