A death in the workplace is never an easy thing to deal with. Since the workplace is oftentimes your home away from home, such a tragedy will always be something that will be hard to accept and move forward from. Sometimes it might be slightly easier to adjust to death after a longtime struggle with a medical condition. But sudden deaths that no one can foresee can be quite a challenge for people to cope with.
When an employee passes away, the first and foremost concern should be to make sure that the family left behind are aware of the benefits that they will get. Companies have policies that assure the next of kin some compensation or assistance on death and disability of illness, especially if these are caused by workplace-related incidents. Or at the very least, the company probably has health and insurance benefits for the employee, even if the death does not necessarily occur at the workplace. Despite the difficult time experienced by the family, at least the company can offer some form of assistance. Co-workers can also pass the hat around, to chip in to help with burial expenses, especially if the insurance policy can't cover all the things that need to be paid.
It would also be good if the deceased's colleagues attended the various services like the wake and the actual funeral. These rituals aren't really for the dead, but rather it is a chance for people who care about the deceased to grieve together, and recall how the person has touched their lives. Some may find this hard, especially those who have been closely working with the deceased person everyday for some time. But attending the services can expose colleagues to the other side of that person - his or her family and other friends who also care about them.
Having one or two co-workers read a eulogy at the memorial would lend an atmosphere of balance, since guests are likely to hear about how the deceased was in his personal life. Showing this concern also sends a message that the company isn't all business - somewhere inside the cold organizational chart lies a heart that cares about everyone in the organization.
The next step is to look for a replacement for the vacated position. As tough as it sounds, the show must go on, and life must go on. As sad as you may be, the company is an entity that waits for no one. It is likely that no one from your existing staff will volunteer, because this might be seen in bad taste. If this is the case, managers can distribute the workload to other employees in the meantime until a suitable replacement has been found.
Death is a part of life, no matter how much we wish that everything would just be all happiness and fun. At the end of the day, what defines a business and its employees is how it can respond to adversity and show appreciation for valued members of the organization.