public abstract class BaseFoo
{
    public BaseFoo()
    {
        FooMethod();
    }

    public abstract void FooMethod();
}

public class Foo : BaseFoo
{
    private Stream _stream;

    public Foo(Stream stream)
    {
        _stream = stream;
    }

    public override void FooMethod()
    {
        //do anything with the stream
        _stream.Read(...);

        //--> _stream = null
    }
}

public Foo(Stream stream)
{
    _stream = stream;

    base();
}

public abstract class BaseFoo
{
    public BaseFoo(bool testToDoSomething)
    {
        FooMethod();
    }

    public abstract void FooMethod();
}

public abstract class BaseFoo
{
    private Action toRunOnConstruct;
    public BaseFoo(Action toRunOnConstruct)
    {
        this.toRunOnConstruct = toRunOnConstruct;
        toRunOnConstruct.Invoke();
    }
}

public class Foo : BaseFoo
{
    private Stream _stream;

    public Foo(Stream stream) : base(()=> SomethingToDoWithTheStream(stream))
    {
        _stream = stream;
    }

    public static void SomethingToDoWithTheStream(Stream stream)
    {
        //do anything with the stream
        stream.Read(...);

        //--> _stream = null
    }