Hydrocarbon wells and methods that utilize a plug with an included tracer material. The hydrocarbon wells include a wellbore that extends within a subsurface region and a downhole tubular that extends within the wellbore and defines a tubular conduit. The hydrocarbon wells also include a plug positioned within the wellbore and a tracer detection structure. The plug forms a fluid seal and includes a tracer material. The tracer detection structure is configured to detect the tracer material within a produced fluid stream that is produced from the hydrocarbon well. The methods include releasing the tracer material from the plug and producing the produced fluid stream. The methods also include detecting the tracer material within the produced fluid stream.