On private property, including your own driveway or a job site you control, Saginaw's streets chapter imposes nothing on a container at all. That is the straightforward half of the answer.
The street is the hard half. The City makes it unlawful for anyone to obstruct, block or barricade a public street or thoroughfare in any manner, and the only exception is for vehicles and pedestrians making lawful use of the roadway. There is no permit in the chapter that a container could be issued under. The permits that do exist cover utility excavations and driveway construction. So in practical terms a container has to go on private ground in Saginaw, and the drop spot is worth planning early.
The larger question is who may deliver one. The City's solid waste ordinance confirms an exclusive franchise for collecting and disposing of waste from premises in the city, and makes it unlawful to engage in that business without a franchise agreement from the City. It then goes further than most cities do: it makes it unlawful for the owner or occupant of any premises to employ anyone other than the franchise holder to collect or dispose of waste, residential or commercial alike. And while the chapter does not reach the occasional cleanup of a property by its own owner or a maintenance worker, the very next sentence states that the chapter does apply to any roll-off container or dumpster, including one used for construction, repair, renovation or demolition work. Dumpsters are named inside the ordinance rather than left to inference.
There is one route the City publishes for a customer, and its limits matter. A business, commercial or industrial occupant can apply to the city secretary for a self-collection and self-disposal permit, which runs for the calendar year, needs a separate application for each separate property, and requires the applicant to describe the vehicles, the containers, the spillage safeguards, the frequency and the final disposal site. The fee is set as a small percentage of what collection service to that property costs, with a floor. Residential premises are expressly excluded from this route altogether.
None of that stops you getting a container in Saginaw, but it does mean the arrangement has to be set up correctly. Applications go to the city secretary at City Hall, P.O. Box 79070, Saginaw, TX 76179. Your account manager establishes which route applies to your project and makes the contact with the City for you before anything is scheduled.