If you're a suitable candidate I'm pretty sure they already explicitly ask you if you'd like to participate.
I'm curious what methods you suggest to make medical trials more safe. In e.g. construction we can regulate personal protection equipment and mandate machines to do the heavy lifting instead of the workers. We can mandate more time off and corporate fitness programs to keep the people healthy. But how would you make a safer clinical trial?
Oh, I had hoped for some proper thoughts on the matter. The first suggestion is too vague and the other two are already the status quo. In fact I have heard (anecdotally) someone got treated for something that, with 99.9% certainty, was unrelated to the clinical trial they, were participating in. But it occurred during the trial, so their health care costs were covered in full by the clinical trial. And if you ever witness that participants of a clinical trial were not fully informed you should report it. The ethics committee and lawmakers take that extremely seriously.
Edit: to better explain my previous point about safety. When we talk about a usual job being dangerous what we mean is that you're supposed to do A, but B might happen and hurt you (build the scaffolding for a house, but pinch your hand when connecting two pieces). Therefore we mandate PPE, maximum working hours, machine assurance, etc. This is possible because the actual job is tangential to the risk associated with it.
A clinical trial is, going from beginning to end: we have simulated this drug in the computer and tested it on cells. Now we need to check for interactions with other parts of the body. For statistically significant results we need 50 animals, we put cancer in them, wait two weeks and then start treating them like we would treat a human who has this cancer. We vary dose and when to give it, maybe the mixture of compounds if the drug is not just a single active component. A lot of the animals will have to be put down when it becomes apparent that this configuration of the drug does not work. But we have a better understanding of the working of the drug in the body now. After that trials move on to human patients. First we start with people who are sick and for whom the current method of treatment did not work. They will die soon anyway, but there is a small chance that the new drug will work on them. Again we vary dose etc, but now we know much better what range of dose is useful. This results in much more difficult to handle data, because taking a few random people will introduce wild variations in confounding factors. But it's a necessary step to show that the drug works in humans, because we can't move on to testing the new drug on people for which the old method of treatment would have worked. After this trial is done it is finally time to try the new drug out on people who come to the hospital to seek treatment. The doctor may offer you the chance to participate in a trial for a new medicine if they think you're a fitting candidate. This trial will test the medicine for the first time against a proper sample of the population. Only now can we say for certain how much better it is than the old drug (or maybe it's worse) and tease out details from the data (e.g. It's usually better, but it's worse if the person has a cold and is overweight when starting treatment. Or it causes severe allergic reactions for people who have asthma that is triggered by grass pollen)
It's important to note that at every step of the process a drug can fail testing. Researchers want the drug to fail early, because every step costs money and time. When we get better simulations or artificial organs to test on they will be used, because it's so much faster and cheaper than going to animal trials with a promising drug, only to find out after three months of hard work that it doesn't work.
Now, the safety concerns in clinical trials is that we have a current drug that works, and we have a new drug that may work. Is it ok to not treat someone with the known working one, just to see if the maybe working one helps? Most people say no. The danger is inherent in the thing, which is why we have such a lengthy process. There is no PPE you can wear to reduce the effects of cancer when the trial requires you to have cancer. We must get to the stage of "it's most likely working better than the current treatment" before starting testing on otherwise healthy humans.