Where on earth have you heard a thing like that?
They can, and have been, and including while still holding office. You do realize that Senator Menendez of New Jersey recently made it through a criminal trial.
Here are a few recent ones:
https://en.wikipedia.org/wiki/List_of_American_federal_politicians_convicted_of_crimes
Steve Stockman (R-TX) was convicted of fraud. (2018)[4]
Anthony Weiner (D-NY)[5] was convicted of sending sexually explicit photos of himself to a 15-year-old girl and was made to sign the sexual offenders register. (2017)[6]
Corrine Brown (D-FL) was convicted on 18 felony counts of wire and tax fraud, conspiracy, lying to federal investigators, and other corruption charges. (2017)[7][8]
Chaka Fattah (D-PA) was convicted on 23 counts of racketeering, fraud, and other corruption charges. (2016)[9]
Dennis Hastert (R-IL) Speaker of the United States House of Representatives pleaded guilty in court for illegally structuring bank transactions related to payment of $3.5 million to quash allegations of sexual misconduct with a student when he was a high school teacher and coach decades ago.[10] (2016)
Michael Grimm (R-NY) pleaded guilty of felony tax evasion. This was the fourth count in a 20-count indictment brought against him for improper use of campaign funds. The guilty plea had a maximum sentence of three years; he was sentenced to eight months in prison. (2015)[11][12]
Trey Radel (R-FL) was convicted of possession of cocaine in November 2013. As a first-time offender, he was sentenced to one year probation and fined $250. Radel announced he would take a leave of absence, but did not resign. Later, under pressure from a number of Republican leaders, he announced through a spokesperson that he would resign. (2013)[13][14][15]
Rick Renzi (R-AZ) was found guilty on 17 of 32 counts against him June 12, 2013, including wire fraud, conspiracy, extortion, racketeering, money laundering and making false statements to insurance regulators. (2013)[16]
Jesse Jackson Jr. (D-IL) pleaded guilty February 20, 2013, to one count of wire and mail fraud in connection with his misuse of $750,000 in campaign funds. Jackson was sentenced to two-and-one-half years' imprisonment. (2013)[17]
Laura Richardson (D-CA) was found guilty on seven counts of violating US House rules by improperly using her staff to campaign for her, destroying the evidence and tampering with witness testimony. The House Ethics Committee ordered Richardson to pay a fine of $10,000. (2012)[18][19]
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