Too strong sentences can indeed lead to more criminals on the loose, as well as more murders. If you've already killed once, there's then no incentive to stop killing. If the cops are after you, you increase your chance of survival by shooting them. If a witness sees you, you might as well kill the witness too.
And then there's a lessened risk of being turned in. Take family situations, for example. Few are willing to turn in a relative if it means life without parole or a death sentence for the relative. That means losing the relative forever.
Too harsh sentencing and especially harsh minimum sentencing because the foam-at-the-mouth public wants revenge, not justice, is particularly a problem with rape sentencing. There, the perpetrator quite often is a family member or loved one. Who goes free because the sentencing is so harsh that the victims won't turn them in.
Yet there are proponents for the death sentence not only for murder, but for rape. Which is truly stupid - that means that a rapist will increase his chances of survival by killing the only witness - the victim.