JIRA filters and Move Issue breaks with field-related stacktrace

A customer reports getting a stacktrace from a particular saved search, and being unable to move an issue to a project. Both errors have the same underlying stacktrace:

java.lang.NullPointerException
at com.atlassian.jira.issue.fields.config.persistence.FieldConfigSchemePersisterImpl.transformToDomainObject(FieldConfigSchemePersisterImpl.java:204)
at com.atlassian.jira.issue.fields.config.persistence.FieldConfigSchemePersisterImpl.getFieldConfigScheme(FieldConfigSchemePersisterImpl.java:159)
at com.atlassian.jira.issue.fields.config.persistence.CachedFieldConfigSchemePersister.getFieldConfigScheme(CachedFieldConfigSchemePersister.java:55)
at com.atlassian.jira.issue.fields.config.manager.CachedFieldConfigSchemeManagerImpl.getValue(CachedFieldConfigSchemeManagerImpl.java:59)
at com.atlassian.jira.issue.fields.config.manager.FieldConfigSchemeManagerImpl.getValue(FieldConfigSchemeManagerImpl.java:67)
at com.atlassian.jira.issue.fields.config.manager.FieldConfigSchemeManagerImpl.getRelevantConfigScheme(FieldConfigSchemeManagerImpl.java:320)
at com.atlassian.jira.issue.fields.config.manager.FieldConfigSchemeManagerImpl.getRelevantConfig(FieldConfigSchemeManagerImpl.java:290)
at com.atlassian.jira.issue.fields.CustomFieldImpl.getRelevantConfig(CustomFieldImpl.java:488)
at com.atlassian.jira.issue.fields.CustomFieldImpl.isInScope(CustomFieldImpl.java:154)
at com.atlassian.jira.issue.fields.layout.field.FieldLayoutImpl.findFields(FieldLayoutImpl.java:211)
at com.atlassian.jira.issue.fields.layout.field.FieldLayoutImpl.getVisibleLayoutItems(FieldLayoutImpl.java:122)
at com.atlassian.jira.web.action.issue.MoveIssueUpdateFields.doDefault(MoveIssueUpdateFields.java:73)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:39)
...