The old man has been living a wifeless existence since his wife passed away.

wifeless 是由名词 wife（妻子）加上后缀 -less 构成的形容词。-less 表示“没有...的”，所以 wifeless 意思是“没有妻子的”，用来形容丧偶或未婚的男性生活状态。