The answer is maybe. It all depends on the type of insurance the company has and what that company deems as covered. In the case of worker's compensation the issuing agency has to investigate the matter to determine liability. If the company is determined to be liable than the loss or damage of a personal property will be covered. If they are deemed as not responsible then you will get nothing. Unfortunately, such matters are determined on a case-by-case basis so it is impossible to say how a specific claim will turn out.
In most cases companies provide their employees with worker's compensation insurance. This is the insurance that covers you and your property. If you are hurt or your property is damaged while onsite than the issuing agency handles the claim and provides compensation if necessary. The insurance the company uses for their building is completely separate. So if the place where you work were to burn down your personal property would not be covered under that policy. Your personal property is covered under worker's compensation So first you need to determine if the company has worker's compensation and then you need to file a claim.
The good news is that a building fire will most likely be covered. So if you leave your tools at work and the building burns down the insurer will compensate you. This is especially true if the items are necessary for your livelihood, and/or the company requires you to store them onsite. Should you accidentally forget your smart phone in your cubicle and someone steals it that is a different case. The issuing company may not compensate you as the folly is mostly on your part. You are not going to know until you file, however, as the results are on a case-by-case basis.