Do you use the suffix of jr or sr for the widow of a deceased person?

Some people continue to use Jr after Sr has died, others do not. Numbering is a completely separate system and does not change when an earlier number dies. John James I is usually the father of John James II but could be an uncle or other older relative. At some point John James II could be John James, Sr to John James III as John James, Jr. Later, after John James II dies, John James III can be Sr to John James IV as Jr. And so forth.