I believe that you can set the default assignee to unassigned, however it is only at the project-level, meaning that you would have to set this for individual projects.
Go to the Administration Screen of your Project, then go to the 'People' tab. You should see the 'Default Asignee :' section there. Click on the pencil icon, and you can choose the default assignee to be Unassigned.
You can find a documentation about this here : https://confluence.atlassian.com/display/JIRA/Defining+a+Project#DefiningaProject-Roles
Allow unassigned issues is by default is set to OFF. switch it to ON.
Then you will be able to see the option unassigned.
If you have problem with configuring, read this
Hope this helps.
I am not sure if my comment would help you. Following worked for me, but please note we do not use ondemand we have Jira installed locally on our server. I do not know how much control you have over ondemand installation.
Use this at your own risk. Make sure that you have "Allow Unassigned Issues" option turned on.
Then edit: [JiraInstallationDir]/atlassian-jira/secure/admin/views/addproject.jsp
Change this line
<aui:component label="'assigneeType'" name="'assigneeType'" template="hidden.jsp" theme="'aui'"/>
to this (add value="'3'")
<aui:component label="'assigneeType'" name="'assigneeType'" template="hidden.jsp" value="'3'" theme="'aui'"/>
for version 5.1.8 it was line 101 in addproject.jsp file. restart Jira.
I hope it works for you.
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