Can you explain that a bit more? How does a company offload costs by freeing their software? Surely they're not expecting to rely on public contributions to reduce maintenance costs, are they?
Even at its most basic, an arbitrary developer filing a bug report is potentially less costly to handle than a customer experiencing a failure...it can be ignored and maybe the developer submits a patch.
On a longer timeline, hiring developers experienced in the technology from the open source community saves on the cost of training them for a proprietary code base.
Ideally, the open source community develops new features, identifies and patchs bugs, writes tests and libraries, etc. adding value realized by the company's paying customers. In the meantime the company still can devote staff to its business priorities and ignore those of the larger community: e.g. no `map` in go-lang and no `react new myapp` at the CLI for React.
To put it another way, why would a business open source code for anything other than business reasons?
On the other hand, there's an intellectual idea that for many companies, existing software should perhaps be seen as a liability in double entry accounting due to it's need for ongoing maintenance, upgrades, potential for catastrophic failure, and the cost associated with alterations for new business processes.
Companies offload some of those costs by open sourcing and allowing developers to happily "give back" to their bottom line.