The pensioner and the 25-year-old, from West Sussex, were held on suspicion of encouraging or assisting a suicide.
Details about the condition of the 71-year-old man have not been disclosed, and none of the family have been named by Sussex Police.
But the force confirmed that officers were having the mental capacity of the "vulnerable" man assessed to determine how able he is to make decisions for himself.
The woman and her son have been freed on police bail until October 8 following their arrest on August 8.
A Sussex Police spokesman said: "It is an offence to encourage or assist suicide under the Coroners and Justice Act 2009, and officers are investigating whether any crime has been committed or is likely to be committed if they do not take action."
Guidelines were issued in February 2010 by the Director of Public Prosecutions Keir Starmer, QC which clarified the position on assisted suicide. It was indicated that anyone acting with compassion to help end the life of someone who has decided they cannot go on would be unlikely to face criminal charges.
Assisted suicide remains a criminal offence in England and Wales, punishable by up to 14 years in prison, but individual decisions on prosecution are now made on the circumstances in each case.
The guideline document was published after a Law Lords ruling in favour of MS sufferer Debbie Purdy who wanted to know whether her husband would be prosecuted for helping her end her life. Dignitas is a Switzerland-based assisted dying group which over the past 14 years has helped more than 1,100 people to die. More than 150 Britons have chosen to die at its clinic in Zurich.
Around 200 people a year end their life there because assisted suicide is legal in Switzerland, as long as the helper does not personally benefit from the death.