They say if the changes go ahead people with asbestos-related diseases will be forced to choose between launching a lawsuit in their lifetime or waiting for their loved ones to do so after they die.
But if they choose the former, their case would probably be heard in a sheriff court or a new personal injury court and they may not be represented by an advocate unless they pay the specialist's fee.
Support groups fear the insurance companies the victims are up against would continue to hire the top lawyers leading to an imbalance in legal representation.
But if they choose not to launch an action and left it to their family, the case could be heard in the Court of Session. There the family would be automatically represented by an advocate.
Lawyers say the dilemma would be a consequence of reforms put forward to move the bulk of cases from the Court of Session in Edinburgh to the sheriff court or a new personal injury court being set up.
The bill raises the minimum level of compensation at stake in civil cases in the Court of Session from £5000 to £150,000.
Laura Blane, a partner with Glasgow law firm Thompsons, who represents families and individuals affected by asbestos, said: "We are concerned about clients' access to justice. Individuals who are dying would have to confront the fact they are dying, decide whether and where to exercise their legal right and whether to exercise that right in their lifetime or wait until their inevitable death.
"We hope ministers will take on board our concerns."
She said campaigners had met with the Scottish Government to raise their fears.
In the Court of Session the individual has an automatic right to be represented by an advocate. The court also has a process to allow asbestos cases to be heard swiftly.
But in the lower courts there is no automatic right to counsel. A person taking action can apply for an entitlement to counsel, but not until the end of the case. The bill allows for the same request to be made at the start of the action.
Ms Blane added: "If someone wants to press on and get a sum of money in life they may be forced to do that in the sheriff court system with all its potential pitfalls." Phyllis Craig, chairwoman of support group Clydeside Action on Asbestos, is due to put her arguments next week to Holyrood's justice committee examining the bill.
A Scottish Government spokeswoman said: "After the process of court reform, asbestosis cases will continue to be able to be raised in the sheriff court, the new specialist personal injury court or the Court of Session depending on the complexity of the case and the value of the damages sought. People will be able to apply to remit cases that become more complex to the Court of Session.
"It is right that complex cases should continue to benefit from counsel's expertise but to allow this to be automatic in every claim could cause undue expense to parties."