The Senate has never voted to remove a member for a health-related cause, although that did happen once in the House (see below). In all the cases cited, control of the Senate or House did not rest on the stricken member's ability to keep his or her seat -- as it now does with the sudden illness of Sen. Tim Johnson (D-SD).
Sen. Joseph Biden (D-DE). After dropping out of the Democratic presidential race in September 1987, Biden complained of severe headaches. He underwent two surgeries to repair aneurisms in arteries supplying blood to his brain. His recuperation kept him away from the Senate for seven months in 1988.
Rep. John Grotberg (R-IL). In January 1986, Grotberg had a heart seizure and lapsed into a coma. The condition was brought on by participation in an experimental program for his colon cancer. His family and staff refused to consider resignation, and he even won the March GOP primary. Grotberg's family finally announced that he would not run again. But he retained his seat until his death in November 1986.
Rep. Gladys Spellman (D-MD). While campaigning in October 1980, Spellman suffered a massive heart attack. Although she never emerged from a semi-conscious, coma-like state, she easily won re-election. But there was no prospect for recovery. The House voted to declare the seat vacant in February 1981. It is the only time lawmakers took action involving an incapacitated member.
Sen. Karl Mundt (R-SD). After a debilitating 1969 stroke, Mundt never returned to work. But he refused to resign, staying in office until his term expired in January 1973. Republicans pressured Mundt to step down shortly before the 1970 elections, when it appeared the GOP was going to lose South Dakota's governorship -- and with it the ability to appoint his Senate successor. There was never talk of a motion to expel, though the Republican Conference eventually stripped Mundt of committee assignments. In November of 1970, South Dakotans elected a Democratic governor, putting an end to the Republican call for Mundt's resignation.
Sen. Clair Engle (D-CA). Democrats pleaded with Engle to resign in the spring of 1964, when he was dying of brain cancer. But Engle refused. In June, when the Senate voted to break the filibuster blocking the civil rights bill, Engle was wheeled onto the floor to vote for cloture by motioning with his hand. He died a month later.
Sen. Carter Glass (D-VA). In the spring of 1943, the 85-year-old Glass stopped coming to work because of his poor health. He kept his seat until his death in May 1946.
Sen. James Grimes (R-IA). An 1869 stroke left Grimes an invalid, according to Sen. Robert Byrd's (D-WV) invaluable book of Senate historical statistics. But Grimes remained in office until his death in February 1872.