The Bible allows a widow to be remarried or to have another husband. If someone loses his or her partner to death and the person wants to remarry, the Bible permits such. There is no offense for someone whose spouse has died, if the person remarries.
Marriage is for companionship. Some people might have their lifespan extended if they have someone who is there to care for them. At our older stage, we do need hands to hold. Loneliness can be traumatic. So, remarrying after the death of one's spouse is not bad.
The Bible warns against fornication and adultery. What of a person whose physical strength is still very much available. Such a person should remarry so that the devil will not tempt him or her. To avoid burning lustfully, let those who which to remarry marry.
