I have a simple class that one of properties is:
public TValue Value => IsSuccess
    ? _value
    : throw new InvalidOperationException("The value of a failure result can not be accessed.");

So it works like this, when some operation is a success assign value from this operation to property easy. But now I when I do sutch a thig:
var result = new Result (someValue) { IsSuccess = false }
var serialized =  JsonConvert.SerializeObject(result); // of course result type is marked as seriazable

So here I am setting such a result to false, and next I want to serilize it, problem is that exception is not serializing and I am getting just thrown exception. What am I missing here?

Serialize property access exception to json
I'm wondering whether there isn't a better design for what you're trying to achieve. Namely, it might be better to move the IsSuccess check logic into a method so that it doesn't get hit during serialization. But if you really decide to do it this way, you could use a JsonConverter to catch and serialize the exception for you:
public class ValueOrExceptionConverter : JsonConverter
{
    public override void WriteJson(JsonWriter writer, object? value, JsonSerializer serializer)
    {
        if (value == null)
        {
            return;
        }

        try
        {
            serializer.Serialize(writer, ((dynamic)value).Value);
        }
        catch (Exception ex)
        {
            serializer.Serialize(writer, new { Value = new { ex.Message } });
        }
    }

    public override object? ReadJson(JsonReader reader, Type objectType, object? existingValue, JsonSerializer serializer)
    {
        throw new NotImplementedException();
    }

    public override bool CanConvert(Type objectType) => true;
}

I'm assuming your Result class is generic so using this converter would look like this:
[JsonConverter(typeof(ValueOrExceptionConverter))]
public class Result<TValue>

This is all assuming that you're using Newtonsoft.Json. The result of using that converter is something like this:
{"Value":"Message":"The value of a failure result can not be accessed."}}

A few notes about the converter code:

Instead of casting to dynamic, you might be better of using an interface or abstract class if you have it. Or if you know exactly which generics you might use for TValue then perhaps you can cast even more specifically.
I've assumed that you don't want to serialize the entire exception. So if you need more than just the Message then you can add those properties like so for example: new { ex.Message, InnerMessage = ex.InnerException.Message }.
I've assumed that the Result class only has one property, named Value. You can add more properties in the same way you can add additional Exception properties.
I haven't implemented the ReadJson because deserializing the exception instead of the value makes that quite tricky. But I'm sure it's not impossible if you need to also deserialize the Result.

