This only applies to the US. The process is similar in Britain, France and Switzerland too. Beyond those countries I’m not sure…
Only the accused can “Plead the 5th (Amendment)” and this does not apply to Civil cases.
In federal cases, a witness that refuses to testify (whether in criminal or civil matters) is subject to fine, an obstruction of justice charge, and in some cases the Attorney General may simply imprison the unwilling witness until he/she comes around.